Single-mode optical fiber with thin coating for high density cables and interconnects

ABSTRACT

An optical fiber is provided that includes a core region, a cladding region having a radius less than about 62.5 microns; a polymer coating comprising a high-modulus layer and a low-modulus layer, wherein a thickness of the low-modulus inner coating layer is in a range of 4 microns to 20 microns, the modulus of the low-modulus inner coating layer is less than or equal to about 0.35 MPa, a thickness of the high-modulus coating layer is in a range of 4 microns to 20 microns, the modulus of the high-modulus inner coating layer is greater than or equal to about 1.6 GPa, and wherein a puncture resistance of the optical fiber is greater than 20 g, and wherein a microbend attenuation penalty of the optical fiber is less than 0.03 dB/km, and wherein an outer diameter of the coated optical fiber is less than or equal to 175 microns

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.17/381,756 filed on Jul. 21, 2021, which claims the benefit of priorityof U.S. Provisional Application Ser. No. 63/054,563 filed on Jul. 21,2020, the contents of which are relied upon and incorporated herein byreference in their entireties for all purposes.

FIELD OF THE DISCLOSURE

This disclosure pertains to single-mode optical fibers. Moreparticularly, this disclosure pertains to small diameter single-modeoptical fibers. Most particularly, this disclosure pertains to smalldiameter single-mode optical fibers having a reduced coating thicknesswithout a significant decrease in puncture resistance

BACKGROUND OF THE DISCLOSURE

Optical fiber technology is penetrating data centers due to cloudcomputing and internet of things that require high bandwidth, reducedlatency, low power consumption, and immunity to EMI/RFI. Futurehyper-scale data centers need special features such as 100K serversspreading over half-million square feet, thus generating a need forincreased capacity, flexibility, and efficiency in the interconnectionschemes within the data center. A large number of interconnects are thusneeded within the data center. Ribbon cables allow higher fiber counts;however, these higher fiber counts will require smaller diameter fibersto fit into the ribbon cables. For example, using a 125 μm overalldiameter bare fiber ribbon cable instead of a 250 μm overall diametertwo-layer acrylate coated fiber ribbon cable results in a volumereduction of at least 75%. However, processing a bare fiber into aribbon cable can cause the breakage of fiber.

In addition, submarine fiber optical cables are designed to carrytelecommunication signals across stretches of land, ocean and sea. Overthe past several years, there has been a dramatic increase intelecommunications signals over submarine cables, with greater thanninety percent of inter-continental communication signals currentlybeing transmitted over these cables. Thus, the demand for thetransmission capacity of such submarine cables has increased, driven bythe growth of internet traffic among different continents. This growthof capacity has traditionally been driven by increasing the bandwidthcapacity of each fiber, for example, but increasing the bit rate orusing dense-wavelength division multiplexing (DWDM), while keeping thefiber count small—typically between four and eight fiber pairs.

However, implementing these advanced transmission technologies hasdriven the electrical power consumption of the optical repeaters in thissystem beyond the level that can be supplied from the terminals. Thispower constraint is forcing submarine system designers to utilize higherfiber counts, and these higher fiber counts will require smallerdiameter fibers to fit into the limited space inside the opticalrepeaters. The cladding diameter of these fibers preferably needs to bemaintained at 125 microns to facilitate fusion splicing to conventionalsingle-mode fibers, which means that the smaller diameter is achieved byreducing the thickness of the protective coating. This thinner coatingneeds to have a high modulus combined with a sufficiently largecross-sectional area to ensure high resistance to punctures andabrasions.

Improvements in the foregoing are desired. Accordingly, the inventorshave developed improved thin-coated single-mode optical fibers that havesufficiently high mechanical reliability.

SUMMARY

According to a first embodiment of the present disclosure, the presentdescription extends to an optical fiber having: a core region; acladding region surrounding the core region, the cladding regioncomprising: an inner cladding directly adjacent to the core region, andan outer cladding surrounding the inner cladding, wherein a radius ofthe cladding region is less than about 62.5 microns; and a polymercoating comprising a high-modulus coating layer surrounding the claddingregion and a low-modulus coating layer disposed between the claddingregion and the high-modulus coating layer, wherein a thickness of thelow-modulus inner coating layer is in a range of 4 microns to 20microns, the modulus of the low-modulus inner coating layer is less thanor equal to about 0.35 MPa, a thickness of the high-modulus coatinglayer is in a range of 4 microns to 20 microns, the modulus of thehigh-modulus inner coating layer is greater than or equal to about 1.6GPa, and wherein a puncture resistance of the optical fiber is greaterthan 20 g, and wherein a microbend attenuation penalty of the opticalfiber is less than 0.03 dB/km, and wherein an outer diameter of thecoated optical fiber is less than or equal to 175 microns, wherein thepuncture resistance of the optical fiber is calculated by equationP_(R)=P₀+C₁E_(s)A_(s), wherein A_(s) is the cross-sectional area of thehigh-modulus coating, wherein Es is the elastic moduli of thehigh-modulus coating, wherein P₀ is a coefficient having a value of 11.3g and C₁ is a coefficient having a value of 2.1 g/MPa/mm², wherein themicrobend attenuation penalty of the optical fiber is calculated byequation:

${{MAP} = {C_{0}f_{0}\sigma\frac{f_{RIP}{f_{g}\left( {E_{g},R_{g}} \right)}{f_{p}\left( {E_{p},t_{p}} \right)}}{f_{CS}\left( {\frac{E_{s}}{E_{p}},R_{s},t_{s}} \right)}}},$

wherein f₀ is the average lateral pressure of the external surface incontact with the high modulus coating, wherein σ is the standarddeviation of the roughness of the external surface in contact with thehigh modulus coating, wherein

${C_{0} = {4 \times {10^{25}\left\lbrack \left( \frac{\pi}{4} \right)^{2.625} \right\rbrack}^{- 1}}},{{{and}{wherein}f_{g}} = \frac{1}{E_{g}^{2}R_{g}^{6}}},{{{and}{wherein}f_{p}} = \frac{E_{p}}{t_{p}^{2}}},{{{and}{wherein}f_{cs}} = {\left\lbrack {1 + {\frac{E_{s}}{E_{p}}\left( \frac{t_{s}}{R_{s}} \right)^{3}}} \right\rbrack^{0.375}\left\{ {\frac{E_{s}}{E_{p}}\left\lbrack {R_{s}^{4} - \left( {R_{s} - t_{s}} \right)^{4}} \right\rbrack} \right\}^{0.625}}},$

wherein R_(g) is the radius of the glass, R_(s) is the outer radius ofthe high-modulus outer coating, t_(p) is the thickness of the innerlow-modulus coating, t_(s) is the thickness of the high-modulus outercoating, E_(g) is the elastic moduli of the glass, E_(p) is the elasticmoduli of the low-modulus inner coating, and E_(S) is the elastic moduliof the high-modulus coating.

According to a second embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the microbend attenuation penaltyof the optical fiber is ≤0.01 dB/km.

According to a third embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the microbend attenuation penaltyof the optical fiber is ≤0.007 dB/km.

According to a fourth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the microbend attenuation penaltyof the optical fiber is ≤0.003 dB/km.

According to a fifth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the puncture resistance of theoptical fiber is ≥25 g.

According to a sixth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the puncture resistance of theoptical fiber is ≥30 g.

According to a seventh embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein a radius of the cladding regionis less than 52.5 microns and the puncture resistance of the opticalfiber is greater than 40 g.

According to a eighth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein the thickness of the high-moduluscoating layer is 9 microns to 18 microns.

According to a ninth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein an attenuation of the opticalfiber is less than 0.20 dB/km.

According to a tenth embodiment of the present disclosure, the opticalfiber of the first embodiment, wherein a mode field diameter of theoptical fiber at 1310 nm is ≥8.6.

According to an eleventh embodiment of the present disclosure thepresent description extends to an optical fiber having: a core region; acladding region surrounding the core region, the cladding regioncomprising: an inner cladding directly adjacent to the core region, andan outer cladding surrounding the inner cladding, wherein a radius ofthe cladding region is between about 45 microns and 55 microns; and apolymer coating comprising a high-modulus coating layer surrounding thecladding region and a low-modulus coating layer disposed between thecladding region and the high-modulus coating layer, wherein a thicknessof the low-modulus inner coating layer is in a range of 6 microns to 20microns, the modulus of the low-modulus inner coating layer is less thanor equal to about 0.35 MPa, a thickness of the high-modulus coatinglayer is in a range of 12 microns to 18 microns, the modulus of thehigh-modulus inner coating layer is greater than or equal to about 1.6GPa, and wherein a puncture resistance of the optical fiber is greaterthan 30 g, and wherein a microbend attenuation penalty of the opticalfiber is less than 0.03 dB/km, and wherein an outer diameter of thecoated optical fiber is less than or equal to 175 microns, wherein thepuncture resistance of the optical fiber is calculated by equationP_(R)=P₀+C₁E_(s)A_(s), wherein A_(S) is the cross-sectional area of thehigh-modulus coating, wherein E_(S) is the elastic moduli of thehigh-modulus coating, wherein P₀ is a coefficient having a value of 11.3g and C₁ is a coefficient having a value of 2.1 g/MPa/mm², wherein themicrobend attenuation penalty of the optical fiber is calculated byequation:

${{MAP} = {C_{0}f_{0}\sigma\frac{f_{RlP}{f_{g}\left( {E_{g},R_{g}} \right)}{f_{p}\left( {E_{p},t_{p}} \right)}}{f_{CS}\left( {\frac{E_{s}}{E_{p}},R_{s},t_{s}} \right)}}},$

wherein f₀ is the average lateral pressure of the external surface incontact with the high modulus coating, wherein σ is the standarddeviation of the roughness of the external surface in contact with thehigh modulus coating, wherein

${C_{0} = {4 \times {10^{25}\left\lbrack \left( \frac{\pi}{4} \right)^{2.625} \right\rbrack}^{- 1}}},{{and}{wherein}}$${}{{f_{g} = \frac{1}{E_{g}^{2}R_{g}^{6}}},{{and}{wherein}}}$${f_{p} = \frac{E_{p}}{t_{p}^{2}}},{{and}{wherein}}$${f_{cs} = {\left\lbrack {1 + {\frac{E_{s}}{E_{p}}\left( \frac{t_{s}}{R_{s}} \right)^{3}}} \right\rbrack^{0.375}\left\{ {\frac{E_{s}}{E_{p}}\left\lbrack {R_{s}^{4} - \left( {R_{s} - t_{s}} \right)^{4}} \right\rbrack} \right\}^{0.625}}},$

wherein R_(g) is the radius of the glass, R_(s) is the outer radius ofthe high-modulus outer coating, t_(p) is the thickness of the innerlow-modulus coating, t_(s) is the thickness of the high-modulus outercoating, E_(g) is the elastic moduli of the glass, E_(p) is the elasticmoduli of the low-modulus inner coating, and E_(S) is the elastic moduliof the high-modulus coating.

According to a twelfth embodiment of the present disclosure, the opticalfiber of the eleventh embodiment, wherein the microbend attenuationpenalty of the optical fiber is ≤0.01 dB/km.

According to a thirteenth embodiment of the present disclosure, theoptical fiber of the eleventh embodiment, wherein the microbendattenuation penalty of the optical fiber is ≤0.007 dB/km.

According to a fourteenth embodiment of the present disclosure, theoptical fiber of the eleventh embodiment, wherein the microbendattenuation penalty of the optical fiber is ≤0.003 dB/km.

According to a fifteenth embodiment of the present disclosure, theoptical fiber of the eleventh embodiment, wherein the punctureresistance of the optical fiber is ≥25 g.

According to a sixteenth embodiment of the present disclosure thepresent description extends to an optical fiber having a core region; acladding region surrounding the core region, the cladding regioncomprising: an inner cladding directly adjacent to the core region, andan outer cladding surrounding the inner cladding; and a polymer coatinghaving a thickness of 25 um or less, wherein the polymer coatingcomprises a high-modulus coating layer surrounding the cladding region,wherein the high-modulus coating layer has a Young's modulus of 1.5 GPaor greater, wherein an outer diameter of the coated optical fiber isless than or equal to 175 microns.

According to a seventeenth embodiment of the present disclosure, theoptical fiber of the sixteenth embodiment, further comprising alow-modulus coating layer surrounding the cladding region, wherein thelow-modulus coating layer has a Young's modulus of 0.5 MPa or less andis disposed between the cladding region and the high-modulus coatinglayer.

According to a eighteenth embodiment of the present disclosure, theoptical fiber of the sixteenth embodiment, wherein a ratio of thethickness of the low-modulus coating layer coating to the thickness ofthe high-modulus coating layer is in the range of 0.8 to 1.2.

According to a nineteenth embodiment of the present disclosure thepresent description extends to a method of coating an optical fiber,comprising: drawing an optical fiber from a draw furnace along a firstvertical pathway;

routing the optical fiber through a coating system wherein a polymercoating is applied to the optical fiber, wherein the coating systemcomprises an entrance, a sizing die having a diameter of 129 μm to 203μm opposite the entrance, and a coating chamber disposed between theentrance and the sizing die, wherein the coating chamber is filled witha coating material in liquid form; and curing the coated optical fiberto form an outer diameter of the coated optical fiber that is less thanor equal to 175 microns.

According to a twentieth embodiment of the present disclosure, theoptical fiber of the nineteenth embodiment, wherein the polymer coatinghas a concentricity of greater than 70%.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from the description or recognized by practicing theembodiments as described in the written description and claims hereof,as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary and are intendedto provide an overview or framework to understand the nature andcharacter of the claims.

The accompanying drawings are included to provide a furtherunderstanding and are incorporated in and constitute a part of thisspecification. The drawings are illustrative of selected aspects of thepresent disclosure, and together with the description serve to explainprinciples and operation of methods, products, and compositions embracedby the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a coated optical fiber in accordance withsome embodiments of the current disclosure.

FIG. 2 is a schematic view of a representative optical fiber ribbon inaccordance with some embodiments of the current disclosure.

FIG. 3 is a schematic view of a representative optical fiber cable inaccordance with some embodiments of the current disclosure.

FIG. 4 depicts a cross-section of a single-mode optical fiber inaccordance with some embodiments of the current disclosure.

FIG. 5 depicts a relative refractive index profile of a single-modeoptical fiber in accordance with some embodiments of the currentdisclosure.

FIG. 6 depicts relative refractive index profiles of optical fibersaccording to embodiments of the present disclosure.

FIG. 7 depicts a relative refractive index profile of an optical fiberaccording to embodiments of the present disclosure.

FIG. 8 depicts the dependence of the puncture load strength as afunction of the cross-sectional area of the high-modulus coatingaccording to the present disclosure.

FIG. 9 depicts a relative refractive index profile of a single-modeoptical fiber in accordance with some embodiments of the currentdisclosure

FIG. 10 is a schematic of core and cladding mode distributions for anoptical fiber with a thick coating in accordance with some embodimentsof the current disclosure.

FIG. 11 is a schematic of core and cladding mode distributions for anoptical fiber with a thin coating in accordance with some embodiments ofthe current disclosure.

FIG. 12 depicts the effects of coating material viscosity and die sizeon the coating thickness in accordance with some embodiments of thecurrent disclosure.

FIG. 13 depicts an exemplary parameter window for forming a targetedfinal coated diameter in accordance with some embodiments of the currentdisclosure.

FIG. 14 depicts the coating thickness standard deviation resulting fromvarious coating material viscosity for different die size systems inaccordance with some embodiments of the current disclosure.

FIG. 15 depicts the effect of drawing speed on coating thickness inaccordance with some embodiments of the current disclosure.

FIG. 16 depicts a graph plotting the correlation between lubricationpressure and the die size for a series of coating material viscosity inaccordance with some embodiments of the current disclosure.

FIG. 17 depicts the correlation between lubrication pressure and drawingspeed in accordance with some embodiments of the current disclosure.

FIG. 18 depicts a relative refractive index profile of a single-modeoptical fiber in accordance with some embodiments of the currentdisclosure.

FIG. 19 depicts the microbend attenuation penalty (MAP) versus thelow-modulus coating thickness for fibers with step-index andtrench-assisted fiber profiles and a cladding diameter of 100 microns inaccordance with some embodiments of the current disclosure.

FIG. 20 depicts the microbend attenuation penalty (MAP) versus thelow-modulus coating thickness for fibers having a trench-assisted fiberprofile and a cladding diameter of 100 microns for different moduli ofthe high-modulus coating in accordance with some embodiments of thecurrent disclosure.

FIG. 21 depicts the puncture resistance versus the low-modulus coatingthickness for fibers having a trench-assisted fiber profile and acladding diameter of 100 microns for different moduli of thehigh-modulus coating in accordance with some embodiments of the currentdisclosure.

FIG. 22 depicts the microbend attenuation penalty (MAP) versus thelow-modulus coating thickness for fibers having a trench-assisted fiberprofile and a cladding diameter of 100 microns for different moduli ofthe low-modulus coating in accordance with some embodiments of thecurrent disclosure.

DETAILED DESCRIPTION

The present disclosure is provided as an enabling teaching and can beunderstood more readily by reference to the following description,drawings, examples, and claims. To this end, those skilled in therelevant art will recognize and appreciate that many changes can be madeto the various aspects of the embodiments described herein, while stillobtaining the beneficial results. It will also be apparent that some ofthe desired benefits of the present embodiments can be obtained byselecting some of the features without utilizing other features.Accordingly, those who work in the art will recognize that manymodifications and adaptations are possible and can even be desirable incertain circumstances and are a part of the present disclosure.Therefore, it is to be understood that this disclosure is not limited tothe specific compositions, articles, devices, and methods disclosedunless otherwise specified. It is also to be understood that theterminology used herein is for the purposes of describing particularaspects only and is not intended to be limiting.

In this specification, and in the claims, which follow, reference willbe made to a number of terms which shall be defined to have thefollowing meanings:

“Optical fiber” refers to a waveguide having a glass portion surroundedby a coating. The glass portion includes a core and a cladding and isreferred to herein as a “glass fiber”.

“Radial position”, “radius”, or the radial coordinate “r” refers toradial position relative to the centerline (r=0) of the fiber.

“Refractive index” refers to the refractive index at a wavelength of1550 nm, unless otherwise specified.

The “refractive index profile” is the relationship between refractiveindex or relative refractive index and radius. For relative refractiveindex profiles depicted herein as having step boundaries betweenadjacent core and/or cladding regions, normal variations in processingconditions may preclude obtaining sharp step boundaries at the interfaceof adjacent regions. It is to be understood that although boundaries ofrefractive index profiles may be depicted herein as step changes inrefractive index, the boundaries in practice may be rounded or otherwisedeviate from perfect step function characteristics. It is furtherunderstood that the value of the relative refractive index may vary withradial position within the core region and/or any of the claddingregions. When relative refractive index varies with radial position in aparticular region of the fiber (e.g. core region and/or any of thecladding regions), it is expressed in terms of its actual or approximatefunctional dependence, or its value at a particular position within theregion, or in terms of an average value applicable to the region as awhole. Unless otherwise specified, if the relative refractive index of aregion (e.g. core region and/or any of the cladding regions) isexpressed as a single value or as a parameter (e.g. Δ or Δ%) applicableto the region as a whole, it is understood that the relative refractiveindex in the region is constant, or approximately constant, andcorresponds to the single value, or that the single value or parameterrepresents an average value of a non-constant relative refractive indexdependence with radial position in the region. For example, if “i” is aregion of the glass fiber, the parameter Δ_(i) refers to the averagevalue of relative refractive index in the region as defined by Eq. (1)below, unless otherwise specified. Whether by design or a consequence ofnormal manufacturing variability, the dependence of relative refractiveindex on radial position may be sloped, curved, or otherwisenon-constant.

“Relative refractive index,” as used herein, is defined in Eq. (1) as:

$\begin{matrix}{{{\Delta_{i}\left( r_{i} \right)}\%} = {100\frac{\left( {n_{i}^{z} - n_{ref}^{z}} \right)}{2n_{i}^{z}}}} & (1)\end{matrix}$

where n_(i) is the refractive index at radial position r_(i) in theglass fiber, unless otherwise specified, and n_(ref) is the refractiveindex of pure silica glass, unless otherwise specified. Accordingly, asused herein, the relative refractive index percent is relative to puresilica glass, which has a value of 1.444 at a wavelength of 1550 nm. Asused herein, the relative refractive index is represented by Δ (or“delta”) or Δ% (or “delta %”) and its values are given in units of “%”,unless otherwise specified. Relative refractive index may also beexpressed as Δ(r) or Δ(r) %.

The average relative refractive index (Δ_(ave)) of a region of the fiberis determined from Eq. (2):

$\begin{matrix}{\Delta_{ave} = {\int_{r_{inner}}^{r_{outer}}\frac{{\Delta(r)}{dr}}{\left( {r_{outer} - r_{inner}} \right)}}} & (2)\end{matrix}$

where ruin e r is the inner radius of the region, r_(outer) is the outerradius of the region, and Δ(r) is the relative refractive index of theregion.

The refractive index of an optical fiber profile may be measured usingcommercially available devices, such as the IFA-100 Fiber Index Profiler(Interfiber Analysis LLC, Sharon, MA USA) or the S14 Refractive IndexProfiler (Photon Kinetics, Inc., Beaverton, OR USA). These devicesmeasure the refractive index relative to a measurement reference index,n(r)-n_(meas), where the measurement reference index n_(meas) istypically a calibrated index matching oil or pure silica glass. Themeasurement wavelength may be 632.5 nm, 654 nm, 677.2 nm, 654 nm, 702.3nm, 729.6 nm, 759.2 nm, 791.3 nm, 826.3 nm, 864.1 nm, 905.2 nm, 949.6nm, 997.7 nm, 1050 nm, or any wavelength therebetween. The absoluterefractive index n(r) is then used to calculate the relative refractiveindex as defined by Eq. (1).

The term “α-profile” or “alpha profile” refers to a relative refractiveindex profile Δ(r) that has the functional form defined in Eq. (3):

$\begin{matrix}{{\Delta(r)} = {{\Delta\left( r_{0} \right)}\left\lbrack {1\ \begin{bmatrix}{❘{r - r_{0}}❘} \\\left( {r_{z} - r_{0}} \right)\end{bmatrix}}^{\alpha} \right\rbrack}} & (3)\end{matrix}$

where r₀ is the radial position at which Δ(r) is maximum, Δ(r₀)>0,r_(Z)>r₀ is the radial position at which Δ(r) decreases to its minimumvalue, and r is in the range r_(i)≤r≤r_(f), where r_(i) is the initialradial position of the α-profile, r_(f) is the final radial position ofthe α-profile, and α is a real number. Δ(r₀) for an α-profile may bereferred to herein as Δ_(max) or, when referring to a specific region iof the fiber, as Δ_(max). When the relative refractive index profile ofthe fiber core region is described by an a-profile with ro occurring atthe centerline (r=0), r_(z) corresponding to the outer radius r₁ of thecore region, and Δ₁(r₁)=0, Eq. (3) simplifies to Eq. (4):

$\begin{matrix}{{\Delta_{1}(r)} = {\Delta_{1\max}\left\lbrack {1 - \left\lbrack \frac{r}{r_{1}} \right\rbrack^{\alpha}} \right\rbrack}} & (4)\end{matrix}$

When the core region has an index described by Eq. (4), the outer radiusri can be determined from the measured relative refractive index profileby the following procedure. Estimated values of the maximum relativerefractive index Δ_(1max), α, and outer radius r_(1est) are obtainedfrom inspection of the measured relative refractive index profile andused to create a trial function Δ_(trial) between r=−r_(1est) andr=r_(1est). Relative refractive index profiles of representative glassfibers having cores described by an α-profile, in accordance withembodiments of the present disclosure, are shown in FIGS. 5 and 6 .

“Trench volume” is defined as:

$\begin{matrix}{V_{Trench} = {❘{2{\int_{r_{{Trench},{inner}}}^{r_{{Trench},{outer}}}{\Delta_{Trench}(r){rdr}}}}❘}} & (5)\end{matrix}$

where r_(Trench,inner) is the inner radius of the trench region of therefractive index profile, r_(Trench,outer) is the outer radius of thetrench region of the refractive index profile, Δ_(Trench)(r) is therelative refractive index of the trench region of the refractive indexprofile, and r is radial position in the fiber. Trench volume is inabsolute value and a positive quantity and will be expressed herein inunits of % Δmicron², % Δ-micron², %Δ-μm², or % Δμm², whereby these unitscan be used interchangeably herein. A trench region is also referred toherein as a depressed-index cladding region and trench volume is alsoreferred to herein as V₃.

The “mode field diameter” or “MFD” of an optical fiber is defined in Eq.(6) as:

MFD=2w

$\begin{matrix}{w^{2} = {2\frac{\int_{0}^{\infty}{\left( {f(r)} \right)^{2}{rdr}}}{\int_{0}^{\infty}{\left( \frac{{df}(r)}{dr} \right)^{2}{rdr}}}}} & (6)\end{matrix}$

where f(r) is the transverse component of the electric fielddistribution of the guided optical signal and r is radial position inthe fiber. “Mode field diameter” or “MFD” depends on the wavelength ofthe optical signal and is reported herein for wavelengths of 1310 nm,1550 nm, and 1625 nm. Specific indication of the wavelength will be madewhen referring to mode field diameter herein. Unless otherwisespecified, mode field diameter refers to the LP₀₁ mode at the specifiedwavelength.

“Effective area” of an optical fiber is defined in Eq. (7) as:

$\begin{matrix}{A_{eff} = \frac{2{\pi\left\lbrack {\int_{0}^{\infty}\left( {{f(r)}^{2}{rdr}} \right.} \right\rbrack}^{2}}{\int_{0}^{\infty}{\left( {f(r)} \right)^{4}{rdr}}}} & (7)\end{matrix}$

where f(r) is the transverse component of the electric field of theguided optical signal and r is radial position in the fiber. “Effectivearea” or “A_(eff)” depends on the wavelength of the optical signal andis understood herein to refer to a wavelength of 1550 nm.

The term “attenuation,” as used herein, is the loss of optical power asthe signal travels along the optical fiber. Attenuation was measured asspecified by the IEC-60793-1-40 standard, “Attenuation measurementmethods.”

The bend resistance of an optical fiber, expressed as “bend loss”herein, can be gauged by induced attenuation under prescribed testconditions as specified by the IEC-60793-1-47 standard, “Measurementmethods and test procedures-Macrobending loss.” For example, the testcondition can entail deploying or wrapping the fiber one or more turnsaround a mandrel of a prescribed diameter, e.g., by wrapping one turnaround either a 15 mm, 20 mm, or 30 mm or similar diameter mandrel (e.g.“1×15 mm diameter bend loss” or the “1×20 mm diameter bend loss” or the“1×30 mm diameter bend loss”) and measuring the increase in attenuationper turn.

“Cable cutoff wavelength,” or “cable cutoff,” as used herein, refers tothe 22 m cable cutoff test as specified by the IEC 60793-1-44 standard,“Measurement methods and test procedures—Cut-off wavelength.”

The optical fibers disclosed herein include a core region, a claddingregion surrounding the core region, and a coating surrounding thecladding region. The core region and cladding region are glass. Thecladding region includes multiple regions. The multiple cladding regionsare preferably concentric regions. The cladding region includes an innercladding region, a depressed-index cladding region, and an outercladding region. The inner cladding region surrounds and is directlyadjacent to the core region. The depressed-index cladding regionsurrounds and is directly adjacent to the inner cladding region suchthat the depressed-index cladding region is disposed between the innercladding and the outer cladding in a radial direction. The outercladding region surrounds and is directly adjacent to thedepressed-index cladding region. The depressed-index cladding region hasa lower relative refractive index than the inner cladding and the outercladding region. The depressed-index cladding region may also bereferred to herein as a trench or trench region. The relative refractiveindex of the inner cladding region may be less than, equal to, orgreater than the relative refractive index of the outer cladding region.The depressed-index cladding region may contribute to a reduction inbending losses and microbending sensitivity. The core region, innercladding region, depressed-index cladding region, and outer claddingregion are also referred to as core, cladding, inner cladding,depressed-index cladding, and outer cladding, respectively.

Whenever used herein, radial position r₁ and relative refractive indexΔ₁ or Δ₁(r) refer to the core region, radial position r₂ and relativerefractive index Δ₂ or Δ₂(r) refer to the inner cladding region, radialposition r₃ and relative refractive index Δ₃ or Δ₃(r) refer to thedepressed-index cladding region, radial position r₄ and relativerefractive index Δ₄ or Δ₄(r) refer to the outer cladding region, radialposition r₅ refers to the optional low-modulus inner coating, radialposition r₆ refers to the high-modulus coating, and the radial positionr₇ refers to the optional pigmented outer coating.

The relative refractive index Δ₁(r) has a maximum value Δ_(1max) and aminimum value Δ_(1min). The relative refractive index Δ₂(r) has amaximum value Δ_(2max) and a minimum value Δ_(2min). The relativerefractive index Δ₃(r) has a maximum value Δ_(3max) and a minimum valueΔ_(3min). The relative refractive index Δ₄(r) has a maximum valueΔ_(4max) and a minimum value Δ_(4min). In embodiments in which therelative refractive index is constant or approximately constant over aregion, the maximum and minimum values of the relative refractive indexare equal or approximately equal. Unless otherwise specified, if asingle value is reported for the relative refractive index of a region,the single value corresponds to an average value for the region.

It is understood that the central core region is substantiallycylindrical in shape and that the surrounding inner cladding region,depressed-index cladding region, outer cladding region, low-moduluscoating, and high-modulus coating are substantially annular in shape.Annular regions are characterized in terms of an inner radius and anouter radius. Radial positions r₁, r₂, r₃, r₄, r₅, r₆ and r₇ referherein to the outermost radii of the core, inner cladding,depressed-index cladding, outer cladding, optional low-modulus innercoating, high-modulus coating, and optional pigmented outer coating,respectively. The radius r₆ also corresponds to the outer radius of theoptical fiber in embodiments without a pigmented outer coating. Thepigmented outer coating may have a high modulus. When a pigmented outercoating is present, the radius r₇ corresponds to the outer radius of theoptical fiber.

When two regions are directly adjacent to each other, the outer radiusof the inner of the two regions coincides with the inner radius of theouter of the two regions. The optical fiber, for example, includes adepressed-index cladding region surrounded by and directly adjacent toan outer cladding region. The radius r₃ corresponds to the outer radiusof the depressed-index cladding region and the inner radius of the outercladding region. The relative refractive index profile also includes adepressed-index cladding region surrounding and directly adjacent to aninner cladding region. The radial position r₂ corresponds to the outerradius of the inner cladding region and the inner radius of thedepressed-index cladding region. Similarly, the radial position ricorresponds to the outer radius of the core region and the inner radiusof the inner cladding region.

The difference between radial position r₂ and radial position r₁ isreferred to herein as the thickness of the inner cladding region. Thedifference between radial position r₃ and radial position r₂ is referredto herein as the thickness of the depressed-index cladding region. Thedifference between radial position r₄ and radial position r₃ is referredto herein as the thickness of the outer cladding region. The differencebetween radial position rs and radial position r₄ is referred to hereinas the thickness of the low-modulus coating. The difference betweenradial position r₆ and radial position r₅ is referred to herein as thethickness of the high-modulus coating.

As will be described further hereinbelow, the relative refractiveindices of the core region, inner cladding region, depressed-indexcladding region, and outer cladding region may differ. Each of theregions may be formed from doped or undoped silica glass. Variations inrefractive index relative to undoped silica glass are accomplished byincorporating updopants or downdopants at levels designed to provide atargeted refractive index or refractive index profile using techniquesknown to those of skill in the art. Updopants are dopants that increasethe refractive index of the glass relative to the undoped glasscomposition. Downdopants are dopants that decrease the refractive indexof the glass relative to the undoped glass composition. In oneembodiment, the undoped glass is silica glass. When the undoped glass issilica glass, updopants include Cl, Br, Ge, Al, P, Ti, Zr, Nb, and Ta,and downdopants include Fluorine and Boron. Regions of constantrefractive index may be formed by not doping or by doping at a uniformconcentration over the thickness of the region. Regions of variablerefractive index are formed through non-uniform spatial distributions ofdopants over the thickness of a region and/or through incorporation ofdifferent dopants in different regions.

Values of Young's modulus, % elongation, and tear strength refer tovalues as determined under the measurement conditions by the proceduresdescribed herein.

Reference will now be made in detail to illustrative embodiments of thepresent description.

One embodiment relates to an optical fiber. The optical fiber includes aglass fiber surrounded by a coating. An example of an optical fiber isshown in schematic cross-sectional view in FIG. 1 . Optical fiber 10includes glass fiber 11 surrounded by an optional low-modulus innercoating 16 and a high-modulus coating 18. In some embodiments,high-modulus coating 18 may include a pigment. Further description ofglass fiber 11, optional low-modulus inner coating 16, and high-moduluscoating 18 is provided below. Additionally, one or more pigmented outercoating layers may surround high-modulus coating 18.

FIG. 2 illustrates an optical fiber ribbon 30, which may include aplurality of optical fibers 20 and a matrix 32 encapsulating theplurality of optical fibers. Optical fibers 20 each include a coreregion, a cladding region, an optional low-modulus inner coating, and ahigh-modulus coating as described above. Optical fibers 20 may alsoinclude a pigmented outer coating as noted above.

As shown in FIG. 2 , optical fibers 20 are aligned relative to oneanother in a substantially planar and parallel relationship. The opticalfibers in fiber optic ribbon 30 are encapsulated by the ribbon matrix 32in any of several known configurations (e.g., edge-bonded ribbon,thin-encapsulated ribbon, thick-encapsulated ribbon, or multi-layerribbon) by conventional methods of making fiber optic ribbons. Fiberoptic ribbon 30 in the embodiment of FIG. 2 contains twelve (12) opticalfibers 20. However, it is contemplated that any number of optical fibers20 (e.g., two or more, four more, six or more, 8 or more, 12 or more, or16 or more) may be employed to form fiber optic ribbon 30 for aparticular use. Ribbon matrix 32 has tensile properties similar to thetensile properties of a high-modulus coating and can be formed from thesame, similar, or different composition used to prepare a high-moduluscoating.

FIG. 3 illustrates an optical fiber cable 40 that includes a pluralityof optical fibers 20 surrounded by jacket 42. In some embodiments,optical fiber cable 40 is a submarine cable. In some embodiments,optical fiber cable 40 is used in fiber ribbons in interconnectionschemes within a data center. Optical fibers 20 may be densely orloosely packed into a conduit enclosed by an inner surface 44 of jacket42. The number of fibers placed in jacket 42 is referred to as the“fiber count” of optical fiber cable 40. As discussed further below, theoptical fibers of the present disclosure have a reduced diameter, thusproviding a high “fiber count.”

The jacket 42 is formed from an extruded polymer material and mayinclude multiple concentric layers of polymers or other materials.Optical fiber cable 40 may include one or more strengthening members(not shown) embedded within jacket 42 or placed within the conduitdefined by inner surface 44. Strengthening members include fibers orrods that are more rigid than jacket 42. The strengthening member may bemade from metal, braided steel, glass-reinforced plastic, fiber glass,or other suitable material. Optical fiber cable 40 may include otherlayers surrounded by jacket 42 such as, for example, armor layers,moisture barrier layers, rip cords, etc. Furthermore, optical fibercable 40 may have a stranded, loose tube core or other fiber optic cableconstruction.

Glass Fiber

As shown in FIG. 1 , glass fiber 11 includes a core region 12 and acladding region 14, as is known in the art. Core region 12 has a higherrefractive index than cladding region 14, and glass fiber 11 functionsas a waveguide. In many applications, core region 12 and cladding region14 have a discernible core-cladding boundary. Alternatively, core region12 and cladding region 14 can lack a distinct boundary.

In some embodiments, core region 12 has a refractive index that varieswith distance from the center of the glass fiber. For example, coreregion 12 may have a relative refractive index profile with an α-profile(as defined by Eq. (3) above) with an α value that is greater than orequal to 2 and less than or equal to 100, or for example an α value thatis greater than or equal to 2 and less than or equal to 10, or greaterthan or equal to 2 and less than or equal to 6, or greater than or equalto 2 and less than or equal to 4, or greater than or equal to 4 and lessthan or equal to 20, or greater than or equal to 6 and less than orequal to 20, or greater than or equal to 8 and less than or equal to 20,or greater than or equal to 10 and less than or equal to 20, or greaterthan or equal to 10 and less than or equal to 40.

A schematic cross-sectional depiction of an exemplary optical fiber isshown in FIG. 4 . In some embodiments, the optical fiber of FIG. 4 maybe used in a submarine cable or to optically connect components in asubmarine repeater. In some embodiments, the optical fiber of FIG. 4 maybe used in data center interconnects. In FIG. 4 , optical fiber 46includes core region 48, cladding region 50, optional low-modulus innercoating 56, and high-modulus coating 58. Cladding region 50 includesinner cladding region 51, depressed-index cladding region 53, and outercladding region 55. A pigmented outer coating layer (e.g. ink layer)optionally surrounds or is directly adjacent to the high-moduluscoating.

As discussed above, optical fiber 46 may have a reduced coatingdiameter. Such reduced diameter(s) may increase the fiber density (e.g.,“fiber count”) of optical fibers 46 when used, for example, in submarinecables or repeaters or data center interconnects. In order to providelow attenuation, large effective area, low bend loss and sufficientlyhigh mechanical reliability with the smaller diameter of optical fiber46, the properties of the fiber are specifically tailored, as discussedfurther below.

A representative relative refractive index profile for a glass fiber,according to embodiments of the present disclosure, is shown in FIG. 5 .The profile of optical fiber 60 of FIG. 5 shows a core region (1) withouter radius r₁ and relative refractive index Δ₁ with maximum relativerefractive index Δ_(1max), an inner cladding region (2) extending fromradial position r₁ to radial position r₂ and having relative refractiveindex Δ₂, a depressed-index cladding region (3) extending from radialposition r₂ to radial position r₃ and having relative refractive indexΔ₃, and an outer cladding region (4) extending from radial position r₃to radial position r₄ and having relative refractive index Δ₄. In theprofile of FIG. 5 , the depressed-index cladding region (3) may bereferred to herein as a trench and has a constant or average relativerefractive index that is less than the relative refractive indices ofthe inner cladding region (2) and the outer cladding region (4). Coreregion (1) has the highest average and maximum relative refractive indexin the profile. In some embodiments, core region (1) may include a lowerindex region at or near the centerline (known in the art as a“centerline dip”) (not shown). In some embodiments, core region (1) mayinclude a higher index region at or near the centerline (referred to asa “centerline spike”) (not shown).

In the relative refractive index profile of FIG. 5 , the core region (1)of the glass fiber has an α-profile with an a value greater than orequal to 2 and less than or equal to 20. The radial position r₀(corresponding to Δ_(1max)) of the a-profile corresponds to thecenterline (r=0) of the fiber and the radial position r_(z) of thea-profile corresponds to the core radius r₁. In embodiments with acenterline dip, the radial position r₀ may be offset from the centerlineof the fiber. In some embodiments, the relative refractive index Δ₁continuously decreases in the radial direction away from the centerline.In other embodiments, relative refractive index Δ₁ varies over someradial positions between the centerline and r₁, and also includes aconstant or approximately constant value over other radial positionsbetween the centerline and r₁.

In FIG. 5 , transition region 61 from inner cladding region (2) todepressed-index cladding region (3) and transition region 62 fromdepressed-index cladding region (3) to outer cladding region (4) areshown as step changes. It is to be understood that a step change is anidealization and that transition region 61 and/or transition region 62may not be strictly vertical in practice as depicted in FIG. 5 .Instead, transition region 61 and/or transition region 62 may have aslope or curvature. When transition region 61 and/or transition region62 are non-vertical, the inner radius r₂ and outer radius r₃ ofdepressed-index cladding region (3) correspond to the mid-points oftransition regions 61 and 62, respectively. The mid-points correspond tohalf of the depth 63 of the depressed-index cladding region (3).

The relative ordering of relative refractive indices Δ₁, Δ₂, Δ₃, and Δ₄in the relative refractive index profile shown in FIG. 5 satisfy theconditions Δ_(1max)>Δ₄>Δ₃ and Δ_(1max)>Δ₂ >Δ₃. The values of Δ₂ and Δ₄may be equal or either may be greater than the other, but both Δ₂ and Δ₄are between Δ_(1max) and Δ₃.

The relative refractive indices Δ₁, Δ₂, Δ₃, and Δ₄ are based on thematerials used in the core region, inner cladding region,depressed-index cladding region, and outer cladding region. Adescription of these material with regard to the relative refractiveindices Δ₁, Δ₂, Δ₃, and Δ₄ is provided below.

While FIG. 5 depicts a schematic cross-sectional depiction of oneexemplary optical fiber, other suitable optical fibers may be used withembodiments described herein. For example, FIG. 9 is a schematiccross-sectional depiction of a generic profile design for a single modefiber that may be used with embodiments described herein. The profile ofthe optical fiber of FIG. 9 shows a core region with outer radius ri andrelative refractive index Δ₁, an inner cladding region extending fromradial position ri to radial position r₂ and having relative refractiveindex Δ₂, a depressed-index cladding region extending from radialposition r₂ to radial position r₃ and having relative refractive indexΔ₃, and an outer cladding region extending from radial position r₃ toradial position r₄ and having relative refractive index Δ₄. Table 1 and2 below depicts various exemplary fiber profile designs that may be usedwith embodiments described herein and Table 3 depicts various opticalproperties of various exemplary optical fiber profile designs that maybe used with embodiments described herein.

TABLE 1 Exemplary Optical Fiber Profile Designs Ex. 1 Ex. 2 Ex. 3 Ex. 4Ex. 5 Ex. 6 Core delta D₁ (%) 0.34 0.29 0.405 0.34 0 0 Alpha 20 20 2.420 20 20 Core radius r₁ (microns) 4.5 4.35 5.9 4.05 4.9 5.9 Innercladding delta D₂ (%) na −0.08 0 0 −0.4 −0.3 Inner cladding radius r₂(microns) na 12 10 9.8 20 22 Trench delta D₃ (%) na na na −0.4 na naTrench radius r₃ (microns) na na na 16 na na Outer cladding delta D₄ (%)0 0 0.05 0 −0.3 −0.2 Cable cutoff (nm) 1208 1205 1196 1210 1405 1472 MFDat 1310 nm (microns) 9.2 8.8 9.2 8.8 9.1 10.7 Aeff at 1310 nm (micron²)66.7 61.9 65.1 60.6 67.6 94.5 Dispersion at 1310 nm (ps/nm · km) 0.330.31 −0.10 −0.25 3.17 3.57 Dispersion slope at 1310 nm (ps/nm² · km)0.0862 0.0844 0.0884 0.0896 0.0855 0.0878 MFD at 1550 nm (microns) 10.410.0 10.5 10.0 10.1 11.8 Aeff at 1550 nm (micron²) 83.1 77.4 82.6 75.880.1 110.8 Dispersion at 1550 nm (ps/nm · km) 17.0 16.3 16.9 17.7 19.820.7 Dispersion slope at 1550 nm (ps/nm² · km) 0.0577 0.0533 0.05790.0645 0.0575 0.0597

TABLE 2 Exemplary Optical Fiber Profile Designs Example 1 Example 2Example 3 Example 4 Example 5 Δ1 (%) 0.399 0.401 0.394 0.391 0.382 r₁(microns) 4.33 4.38 4.26 4.37 4.29 Alpha 10.07 10.28 11.32 10.85 9.81 Δ2(%) 0 0 0 0 0 Δ3 (%) −0.443 −0.394 −0.383 −0.417 −0.292 r₂ (microns)9.04 9.38 10.47 10.19 10.64 r₃ (microns) 14.71 14.90 15.88 16.28 17.83Trench Volume (%-microns²) 59.7 52.8 54.6 67.1 59.8 MFD at 1310 nm(microns) 8.45 8.50 8.52 8.59 8.61 MFD at 1550 nm (microns) 9.43 9.499.61 9.65 9.76 Dispersion at 1310 nm 0.56 0.51 −0.18 0.22 −0.47(ps/nm/km) Slope at 1310 nm (ps/nm²/km) 0.090 0.090 0.088 0.089 0.088Zero Dispersion Wavelength (nm) 1304 1304 1312 1307 1315 TheoreticalCutoff (nm) 1245 1269 1248 1264 1224 Fiber Cutoff (nm) 1240 1260 12401260 1220 Bend Loss at 1550 nm for 10 mm 0.049 0.072 0.082 0.03 0.078diam. mandrel (dB/turn) Example 6 Example 7 Example 8 Example 9 Example10 Δ1 (%) 0.371 0.382 0.368 0.352 0.334 r₁ (microns) 4.37 4.70 4.51 4.514.57 Alpha 10.48 7.74 9.97 10.07 11.00 Δ2 (%) 0 0 0 0 0 Δ3 (%) −0.375−0.385 −0.333 −0.360 −0.365 r₂ (microns) 9.61 11.02 9.98 9.93 10.19 r₃(microns) 14.28 15.13 15.27 14.59 14.62 Moat Volume (%-microns²) 41.841.4 44.5 41.2 40.1 MFD at 1310 nm (microns) 8.71 8.83 8.84 8.96 9.17MFD at 1550 nm (microns) 9.77 9.91 9.91 10.05 10.29 Dispersion at 1310nm 0.28 0.46 0.46 0.47 0.59 (ps/nm/km) Slope at 1310 nm (ps/nm²/km)0.090 0.089 0.089 0.090 0.090 Zero Dispersion Wavelength (nm) 1307 13051305 1305 1303 Theoretical Cutoff (nm) 1224 1305 1254 1228 1219 FiberCutoff (nm) 1210 1280 1240 1210 1200 Bend Loss at 1550 nm for 10 0.320.2 0.234 0.446 0.672 mm diam. mandrel (dB/turn)

TABLE 3 Optical Properties of Exemplary Optical Fiber Profile Low- High-Modulus Modulus Attenuation Glass Coating Coating (dB/km) Cable MFD (μm)Diameter Diameter Diameter 1310 1550 cutoff 1310 1550 (μm) (μm) (μm) nmnm (nm) nm nm 125 NA 140 0.355 0.215 1240 9.38 10.64 125 133 142 0.3240.191 1170 9.27 10.97 125 155 175 0.354 0.21 1140 9.41 10.61 115.5 NA125 0.351 0.223 125 NA 140 0.339 0.206 1170 9.06 125 NA 140 0.344 0.2211210 125 NA 140 0.336 0.207 1200 125 NA 140 0.339 0.206 1220 9.28 10.56125 NA 155 0.333 0.214 125 NA 132 125 NA 140 118 NA 121 0.964 2.01 11409.07 10.46 106 NA 125 0.874 4.32 980 110 NA 126 0.581 1.238 1090 8.719.92 125 NA 132 0.596 0.775 125 NA 140 0.551 0.747 1190 9.44 125 NA 1400.483 0.582 9.2 10.59 125 NA 155 0.439 0.413 1230 125 NA 175 0.527 0.7321170 9.46 10.51 125 155 175 0.42 0.284 1150 9.3 10.49

Core Region

The core region comprises silica glass. The silica glass of the coreregion may be undoped silica glass, updoped silica glass, and/ordowndoped silica glass. Updoped silica glass includes silica glass dopedwith an alkali metal oxide (e.g. Na₂O, K₂O, Li₂O, Cs₂O, or Rb₂O).Downdoped silica glass includes silica glass doped with F. In oneembodiment, the silica glass of the core region may be Ge-free and/orCl-free; that is the core region comprises silica glass that lacks Geand/or Cl.

Additionally, or alternatively, the core region may comprise silicaglass doped with at least one alkali metal, such as, lithium (Li),sodium (Na), potassium (K), rubidium (Rb), cesium (Cs) and/or francium(Fr). In some embodiments, the silica glass is doped with a combinationof sodium, potassium, and rubidium. The silica glass may have a peakalkali concentration in the range from about 10 ppm to about 500, or inthe range from about 20 ppm to about 450 ppm, or in the range from about50 ppm to about 300 ppm, or in the range from about 10 ppm to about 200ppm, or in the range from about 10 ppm to about 150 ppm. The alkalimetal doping within the disclosed ranges results in lowering of Rayleighscattering, thereby proving a lower optical fiber attenuation.

In some embodiments, the core region comprises silica glass doped withan alkali metal and doped with F as a downdopant. The concentration of Fin the core of the fiber is in the range from about 0.1 wt % to about2.5 wt %, or in the range from about 0.25 wt % to about 2.25 wt %, or inthe range from about 0.3 wt % to about 2.0 wt %.

In other embodiments, the core region comprises silica glass doped withGe and/or Cl. The concentration of GeO₂ in the core of the fiber may bein a range from about 2.0 to about 8.0 wt %, or in a range from about3.0 to about 7.0 wt %, or in a range from about 4.0 to about 6.5 wt.%.The concentration of Cl in the core of the fiber may be in a range from1.0 wt % to 6.0 wt %, or in a range from 1.2 wt % to 5.5 wt %, or in arange from 1.5 wt % to 5.0 wt %, or in a range from 2.0 wt % to 4.5 wt%, or greater than or equal to 1.5 wt % (e.g., ≥2 wt %, ≥2.5 wt %, ≥3 wt%, ≥3.5 wt %, ≥4 wt %, ≥4.5 wt %, ≥5 wt %, etc.).

In embodiments where the core is substantially free of Ge or Cl, therelative refractive index Δ₁ or Δ_(1max) of the core region is in therange from about −0.10% to about 0.20%, or in the range from about−0.05% to about 0.15%, or in the range from about 0.0% to about 0.10%.The minimum relative refractive index Δ_(1min) of the core is in therange from about −0.20% to about −0.50%, or in the range from about−0.30% to about −0.40%, or in the range from about −0.32% to about−0.37%. The difference Δ_(1max) to Δ_(1min) is greater than 0.05%, orgreater than 0.10%, or greater than 0.15%, or greater than 0.20%, or inthe range from 0.05% to 0.40%, or in the range from 0.10% to 0.35%.

In embodiments where the core is doped with Ge and/or Cl, the relativerefractive index Δ₁ or Δ_(1max) of the core region is in the range fromabout 0.20% to about 0.45%, or in the range from about 0.25% to about0.40%, or in the range from about 0.30% to about 0.38%. The minimumrelative refractive index Δ_(1min) of the core is in the range fromabout −0.05% to about −0.05%, or in the range from about −0.03% to about0.03%, or in the range from about −0.02% to about 0.02%. The differenceΔ_(1max) to Δ_(1min) is greater than 0.20%, or greater than 0.25%, orgreater than 0.30%, or in the range from 0.25% to 0.45%, or in the rangefrom 0.30% to 0.40%.

The radius r₁ of the core region is in the range from about from about3.0 microns to about 6.5 microns, or in the range from about 3.5 micronsto about 6.0 microns, or in the range from about 4.0 microns to about6.0 microns, or in the range from about 4.5 microns to about 5.5microns. In some embodiments, the core region includes a portion with aconstant or approximately constant relative refractive index that has awidth in the radial direction of at least 1.0 micron, or at least 2.0microns, or at least 3.0 microns, or in the range from 1.0 microns to3.0 microns, or in the range from 2.0 microns to 3.0 microns. In someembodiments, the portion of the core region having a constant orapproximately constant relative refractive index has a relativerefractive index of Δ_(1min).

Inner Cladding Region

In embodiments in which the core is substantially free of Ge and Cl, theinner cladding region is comprised of downdoped silica glass that isdoped with F. The average concentration of downdopant in the innercladding region is greater than the average concentration of downdopantin the core region.

The relative refractive index Δ₂ or Δ_(2max) of the inner claddingregion is in the range from about −0.20% to about −0.50%, or in therange from about −0.25% to about −0.45%, or in the range from about−0.30% to about −0.40%, or in the range from about −0.33% to about−0.37%. The relative refractive index 42 is preferably constant orapproximately constant. The difference Δ_(1max)-Δ₂ (or the differenceΔ_(1max)-Δ_(2max)) is greater than about 0.25%, or greater than about0.30%, or greater than about 0.35%, or in the range from about 0.25% toabout 0.45%, or in the range from about 0.30% to about 0.40%.

The radius r₂ of the inner cladding region is in the range from about7.0 microns to about 15.0 microns, or in the range from about 7.5microns to about 13.0 microns, or in the range from about 8.0 microns toabout 12.0 microns, or in the range from about 8.5 microns to about 11.5microns, or in the range from about 9.0 microns to about 11.0 microns,or in the range from about 9.5 microns to about 10.5 microns. Thethickness r₂-r₁ of the inner cladding region is in the range from about3.0 microns to about 10.0 microns, or from about 4.0 microns to about9.0 microns, or from about 4.5 microns to about 7.0 microns.

In embodiments in which the core is doped with Ge and/or Cl, the innercladding region comprises silica that is substantially free of Ge and/orCl. The relative refractive index Δ₂ or Δ_(2max) of the inner claddingregion is in the range from about −0.05% to about −0.05%, or in therange from about −0.03% to about 0.03%, or in the range from about−0.02% to about 0.02%. The relative refractive index Δ₂ is preferablyconstant or approximately constant. The difference Δ_(1max)-Δ₂ (or thedifference Δ_(1max)-Δ_(2max)) is greater than about 0.20%, or greaterthan about 0.25%, or greater than about 0.30%, or in the range fromabout 0.25% to about 0.40%, or in the range from about 0.30% to about0.38%.

The radius r₂ of the inner cladding region is in the range from about8.0 microns to about 16.0 microns, or in the range from about 9.0microns to about 15.0 microns, or in the range from about 10.0 micronsto about 14.0 microns, or in the range from about 10.5 microns to about13.5 microns, or in the range from about 11.0 microns to about 13.0microns. The thickness r₂-r₁ of the inner cladding region is in therange from about 3.0 microns to about 10.0 microns, or from about 4.0microns to about 9.0 microns, or from about 5.0 microns to about 8.0microns.

Depressed-Index Cladding Region

The depressed-index cladding region comprises downdoped silica glass. Asdiscussed above, the preferred downdopant is fluorine. The concentrationof fluorine in the depressed-index cladding region is in the range fromabout 0.30 wt % to about 2.50 wt %, or in the range from about 0.60 wt %to about 2.25 wt %, or in the range from about 0.90 wt % to about 2.00wt %.

The relative refractive index Δ₃ or Δ_(3min) is in the range from about−0.30% to about −0.80% or in the range from about −0.40% to about−0.70%, or in the range from about −0.50% to about −0.65%. The relativerefractive index Δ₃ is preferably constant or approximately constant.The difference Δ_(1max)-Δ₃ (or the difference Δ_(1max)-Δ_(3min), or thedifference Δ₁-Δ₃, or the difference Δ₁-Δ_(3min)) is greater than about0.50%, or greater than about 0.55%, or greater than about 0.6%, or inthe range from about 0.50% to about 0.80%, or in the range from about0.55% to about 0.75%. The difference Δ₂-Δ₃ (or the differenceΔ₂-Δ_(3min), or the difference Δ_(2max)-Δ₃, or the differenceΔ_(2max)-Δ_(3min)) is greater than about 0.10%, or greater than about0.20%, or greater than about 0.30%, or in the range from about 0.10% toabout 0.70%, or in the range from about 0.20% to about 0.65%.

The inner radius of the depressed-index cladding region is r₂ and hasthe values specified above. The outer radius r₃ of the depressed-indexcladding region is in the range from about 10.0 microns to 20.0 microns,or in the range from about 12.0 microns to about 19.5 microns, or in therange from about 13.0 microns to about 19.0 microns, or in the rangefrom about 13.5 microns to about 18.5 microns, or in the range fromabout 14.0 microns to about 18.0 microns, or in the range from about14.5 microns to about 17.5 microns. The thickness r₃-r₂ of thedepressed-index cladding region is in the range from 1.0 microns to 12.0microns, or in the range from about 2.0 microns to about 10.0 microns,or in the range from about 2.5 microns to about 9.0 microns, or in therange from about 3.0 microns to about 8.0 microns.

The depressed-index cladding region may be an offset trench design witha trench volume of about 30% Δ-micron² or greater, or about 50%Δ-micron² or greater, or about 75% Δ-micron² or less, or about 30%Δ-micron² or greater and about 75% Δ-micron² or less, or about 50%Δ-micron² or greater and about 75% Δ-micron² or less. Trench volumeslower than the disclosed ranges have reduced bending performance, andtrench volumes higher than the disclosed ranges no longer operate assingle-mode fibers.

The offset trench designs disclosed herein include an inner claddingregion. Furthermore, the offset trench designs disclosed herein provideadvantages over traditional trench designs that are adjacent to the coreregion. More specifically, the offset trench designs disclosed hereinreduce confinement of the fundamental mode and provide improved bendloss at large bend diameters (e.g., bend diameters >25 mm) for targetoptical fiber mode field diameter and cable cutoff characteristics.Furthermore, the trench designs disclosed herein have a depressed indextrench region, which advantageously confines the intensity profile ofthe fundamental LP01 mode propagating through the optical fiber, therebyreducing the optical fiber mode field diameter.

Outer Cladding Region

In embodiments in which the core is substantially free of Ge and Cl, theouter cladding region comprises downdoped silica glass. The preferreddowndopant is fluorine. The concentration of fluorine in the outercladding region is in the range from about 0.30 wt % to about 2.20 wt %,or in the range from about 0.60 wt % to about 2.00 wt %, or in the rangefrom about 0.90 wt % to about 1.80 wt %. The relative refractive indexΔ₄ or Δ_(4max) of the outer cladding region is in the range from about−0.20% to about −0.50%, or in the range from about −0.25% to about−0.45%, or in the range from about −0.30% to about −0.40%, or in therange from about −0.33% to about 0.37%. The relative refractive index Δ₄is preferably constant or approximately constant. As shown in FIG. 5 ,the relative refractive index Δ₄ may be approximately equal to therelative refractive index Δ₂.

In an embodiment, the outer cladding is substantially pure silica.Alternatively, the outer cladding may be doped with Cl to a relativerefractive index in the range from about 0.01% to about 0.1%, or fromabout 0.02% to about 0.08%, or from about 0.03% to about 0.06%. Theconcentration of Cl in the outer cladding may range from about 0.1 wt %to about 1.0 wt %, from about 0.2 wt % to about 0.8 wt %, or from about0.3 wt % to about 0.6 wt %. Alternatively, the outer cladding may bedoped with Titania to strengthen the cladding surface so as to stopdefects such as scratches from propagating through the fiber. In someembodiments, the outer cladding may be doped with a Titaniaconcentration of about 5 wt % to about 25 wt %.

The inner radius of the outer cladding region is r₃ and has the valuesspecified above. In some embodiments, the outer radius r₄ is about 62.5microns to facilitate splicing to conventional 125 micron claddingdiameter fibers using cladding-alignment splicers. The outer radius r₄of the outer cladding region is in the range from 60.0 microns to 65.0microns, or in the range from 61.0 microns to 64.0 microns, or in therange from 62.0 microns to 63.0 microns, or in the range from 62.25microns to 62.75 microns. Thus, for example, the diameter of thecladding region (i.e., outer radius r₄ multiplied by 2) in the rangefrom 120.0 microns to 130.0 microns, or in the range from 122.0 micronsto 128.0 microns, or in the range from 124.0 microns to 126.0 microns,or in the range from 124.5 microns to 125.5 microns. The thickness r₄-r₃of the outer cladding region is in the range from about 20.0 microns toabout 60.0 microns, or in the range from about 30.0 microns to about55.0 microns, or in the range from about 40.0 microns to about 50.0microns. In some embodiments, the outer radius r₄ is about 50 microns toenable the thickness of the low-modulus and high-modulus coatings to beincreased. The outer radius r₄ of the outer cladding region is in therange from 45.0 microns to 55.0 microns, or in the range from 49.0microns to 51.0 microns, or in the range from 49.5 microns to microns,or in the range from 49.65 microns to 50.35 microns. Thus, for example,the diameter of the cladding region (i.e., outer radius r₄ multiplied by2) in the range from 90.0 microns to 110.0 microns, or in the range from98.0 microns to 102.0 microns, or in the range from 99.0 microns to101.0 microns, or in the range from 99.3 microns to 100.7 microns. Thethickness r₄-r₃ of the outer cladding region is in the range from about20.0 microns to about microns, or in the range from about 25.0 micronsto about 45.0 microns, or in the range from about 30.0 microns to about40.0 microns.

Optical Fiber Characteristics

The optical fibers according to the embodiments of the presentdisclosure may have a mode field diameter in the range of about 9.0microns to about 10.0 microns at 1310 nm and in the range of about 10.0microns to about 11.0 microns at 1550 nm with a cable cutoff of lessthan about 1520 nm. In some embodiments, the 22-meter cable cutoffwavelength is less than about 1500 nm, or less than about 1450 nm, orless than about 1400 nm, or less than about 1300 nm, or less than about1260 nm. In some embodiments, the 2-meter fiber cutoff wavelength isless than about 1520 nm, or less than about 1500 nm, or less than about1450 nm, or less than about 1400 nm, less than about 1300 nm, or lessthan about 1260 nm.

Additionally, optical fibers according to the embodiments of the presentdisclosure may have an effective area at 1550 nm greater than about 75.0micron², greater than about 80 micron², or greater than about 85micron², or in the range of about 75 micron² to about 95 micron², or inthe range from about 80 micron² to about 90 micron², or about 85 micron²to about 90 micron².

The attenuation of the optical fibers disclosed herein is less than orequal to 0.36 dB/km at a wavelength of 1310 nm, or less than or equal to0.30 dB/km, or less than or equal to dB/km, or less than or equal to0.26 dB/km at a wavelength of 1310 nm. The attenuation of the opticalfibers disclosed herein is less than or equal to 0.24 dB/km, or lessthan or equal to dB/km, or less than or equal to 0.20 dB/km at awavelength of 1550 nm.

As shown in FIG. 5 , optical fiber 60 provides an exemplary embodimentof an optical fiber with an alkali doped core, a relative refractiveindex Δ₁ of the core region (1) between about −0.3% to about −0.42%, anda core radius (r₁) between about 4 microns and about 6.5 microns.Additionally, an inner cladding region thickness of optical fiber 60 isbetween about 2 microns and about 12 microns. Optical fiber 60 has anoff-set trench design with a trench volume of 54.5% Δ-micron². Thecladding of optical fiber 60 is fluorine-doped and the depressed-indexcladding region has a radius (r₃) of about 17.5 microns. The opticalproperties of optical fiber 60 are shown in Table 4 below.

TABLE 4 Optical Properties of Optical Fiber 60 Mode Field Diameter (at1310 nm) 9.22 microns Mode Field Diameter (at 1550 nm) 10.27 micronsMode Field Diameter (at 1625 nm) 10.61 microns Zero DispersionWavelength 1319 nm Cable Cutoff 1315 nm Trench Volume 54.5% Δ-micron² 15mm Diameter Bend Loss 0.04 dB/turn 20 mm Diameter Bend Loss 0.009dB/turn 30 mm Diameter Bend Loss 0.001 dB/turn

FIG. 6 depicts second and third exemplary embodiments of optical fibers,64 and 65, with an alkali doped core and a trench volume of greater thanabout 50% Δ-micron², and wherein the cladding is fluorine doped and thedepressed-index cladding region has a radius (r₃) of about 17.5 microns.As shown in Table 5 below, optical fiber 64 results in a mode fielddiameter of 9.07 microns at 1310 nm, and optical fiber 65 results in amode field diameter of 9.39 microns at 1310 nm. The optical propertiesof optical fibers 64 and 65 are shown in Table 2 below.

TABLE 5 Optical Properties of Optical Fibers 64 and 65 Optical Fiber 64Optical Fiber 65 Mode Field Diameter (at 1310 nm) 9.07 microns 9.39microns Mode Field Diameter (at 1550 nm) 10.08 microns 10.48 micronsMode Field Diameter (at 1625 nm) 10.41 microns 10.83 microns ZeroDispersion Wavelength 1319 nm 1320 nm Cable Cutoff 1419 nm 1339 nmTrench Volume 55% Δ-micron² 55% Δ-micron² 15 mm Diameter Bend Loss0.0137 dB/turn 0.042 dB/turn 20 mm Diameter Bend Loss 0.0003 dB/turn0.009 dB/turn 30 mm Diameter Bend Loss 0.0002 dB/turn 0.001 dB/turn

FIG. 7 depicts an embodiment of an optical fiber 66 with a Ge-dopedcore, a trench volume of greater than 50% Δ-micron², and wherein theinner and cladding regions are substantially pure silica and thedepressed-index cladding region has a radius (r₃) of about 16.8 microns.As shown in Table 6 below, optical fiber 64 results in a mode fielddiameter of 10.6 microns at a wavelength of 1550 nm. The refractiveindex profile parameters and optical properties of optical fiber 66 areshown in Table 6 below.

TABLE 6 Optical Properties of Optical Fiber 66 Fiber 66 Δ₁ (%) 0.35 r₁(microns) 5.35 Core alpha 3.0 Δ₂ (%) 0.01 r₂ (microns) 12.0 Δ₃ (%) −0.46r₃ (microns) 16.8 V₃ (%-microns²) 63.6 r₄ (microns) 62.5 r₆ (microns)80.9 MFD at 1550 nm (microns) 10.6 Aeff at 1550 nm (microns²) 85.5Dispersion at 1550 nm (ps/nm/km) 18.3 Dispersion at 1310 nm (ps/nm/km)0.38 Zero Dispersion Wavelength (nm) 1306 Attenuation at 1550 nm (dB/km)0.23 22 m Cable Cutoff Wavelength (nm) 1287  2 m Fiber Cutoff Wavelength(nm) 1338 1 × 10 mm diameter macrobend loss at 1550 0.6 nm (dB) 1 × 15mm diameter macrobend loss at 1550 0.07 nm (dB)

The off-set trench design of optical fibers 60, 64, 65 and 66 provideimproved bend performance for the smaller diameter fibers disclosedherein. More specifically, the off-set trench design disclosed hereinprovides low attenuation, large effective area, and low bend loss in acompact form, with a cladding diameter of about 125 microns and an outercoating diameter less than 175 microns.

Coating Properties

The transmissivity of light through an optical fiber is highly dependenton the properties of the coatings applied to the glass fiber. Asdiscussed above (and with reference to FIG. 4 ), the coatings mayinclude an optional low-modulus inner coating 56 and a high-moduluscoating 58, where the high-modulus coating surrounds the optionallow-modulus inner coating and the optional low-modulus inner coatingcontacts the glass fiber (which includes a central core regionsurrounded by a cladding region). An optional pigmented outer coatinglayer (e.g. ink layer) surrounds and directly contacts the high-moduluscoating.

High-modulus coating 58 is a harder material (higher Young's modulus)than the optional low-modulus coating 56 and is designed to protect theglass fiber from damage caused by abrasion or external forces that ariseduring processing, handling, and deployment of the optical fiber.Optional low-modulus inner coating 56 is a softer material (lowerYoung's modulus) than high-modulus coating 58 and is designed to bufferor dissipates stresses that result from forces applied to the outersurface of the high-modulus coating. The optional low-modulus coatingmay help dissipate stresses that arise due to the microbends the opticalfiber encounters when deployed in a cable but is not essential for shortlength applications such as optical interconnects. The microbendingstresses transmitted to the glass fiber need to be minimized becausemicrobending stresses create local perturbations in the refractive indexprofile of the glass fiber. The local refractive index perturbationslead to intensity losses for the light transmitted through the glassfiber. By dissipating stresses, the optional low-modulus coatingminimizes intensity losses caused by microbending.

A thinner coating on the optical fiber is considered to increasemicrobending loss because it provides less protection against externalperturbations. These perturbations result in power coupling from thelight guided in the core (core mode) to higher-order modes in thecladding (cladding mode). As shown in FIG. 10 , the cladding mode canhave significant overlap with the coating layer which has highabsorption. This process of coupling and absorption by the coatingmaterials result in optical power loss.

An approach for quantifying the microbending loss of an optical fiber onthe properties of the coatings is published in the article entitled“Relationship of Mechanical Characteristics of Dual Coated Single ModeFibers and Microbending Loss,” by J. Baldauf, N. Okada and M. Miyamoto,in IEICE Trans. Commun., Vol. E76-B, No. 4, pp. 352-357 (April, 1993).The authors introduced a parameter X_(s), which is an effective springconstant for the force that couples the secondary (high-modulus) coatingand the glass fiber. This spring constant parameterization providesqualitative guidance that a thick primary (low-modulus) coating with alow modulus provides better microbending performance, but it does notfully capture the contributions of the glass and the high-moduluscoating.

The combined roles of the glass, low-modulus inner coating, andhigh-modulus coating result in a microbending attenuation penalty (MAP)of:

$\begin{matrix}{{MAP} = {C_{0}f_{0}\sigma\frac{f_{RIP}{f_{g}\left( {E_{g},R_{g}} \right)}{f_{p}\left( {E_{p},t_{p}} \right)}}{f_{CS}\left( {\frac{E_{s}}{E_{p}},R_{s},t_{s}} \right)}}} & (8)\end{matrix}$

where f₀ and σ are the average lateral pressure and standard deviationof the roughness of the external surface in contact with thehigh-modulus coating, respectively, and

$C_{0} = {4 \times {{10^{25}\left\lbrack \left( \frac{\pi}{4} \right)^{2.625} \right\rbrack}^{- 1}.}}$

f_(RIP) accounts for the role of the refractive index profile and is oforder unity. Attenuation data indicates that f_(RIP) is approximately1.0 for single-mode fiber with a step-index refractive index profile andis about 0.5 for bend-insensitive single-mode fibers with refractiveindex profiles that include a depressed index trench in the cladding.The other three terms in Eq. 8 are the contributions of the glass,low-modulus inner coating and the system comprising the low-modulusinner coating and high-modulus coating to the microbending response andare given by:

${f_{g} = \frac{1}{E_{g}^{2}R_{g}^{6}}},$${f_{p} = \frac{E_{p}}{t_{p}^{2}}},$${{{and}f_{cs}} = {\left\lbrack {1 + {\frac{E_{s}}{E_{p}}\left( \frac{t_{s}}{R_{s}} \right)^{3}}} \right\rbrack^{0.375}\left\{ {\frac{E_{s}}{E_{p}}\left\lbrack {R_{s}^{4} - \left( {R_{s} - t_{s}} \right)^{4}} \right\rbrack} \right\}^{{0.6}25}}},$

where R_(g) is the radius of the glass (i.e. the outer radius of theouter cladding region), R_(s) is the outer radius of the high-modulusouter coating, t_(p) is the thickness of the inner low-modulus coating,t_(s) is the thickness of the high-modulus outer coating, and E_(g),E_(p) and E_(s) are the elastic moduli of the glass, low-modulus innercoating and high-modulus coating, respectively. The MAP has units ofdB/km when the units for the moduli and radii are GPa and microns,respectively. The low-modulus inner coating coefficient f_(p) depends on(1/t_(p))², rather than on just 1/t_(p), as predicted by the springconstant parameterization. The f_(cs) coating system coefficient is ofinterest for fibers with thinner coatings because it is very large whenthe high-modulus coating is relative thick (t_(s) is greater than about20 microns), which corresponds to a low MAP. However, it becomes quitesmall and yields a MAP value greater than 0.01 dB/km when thehigh-modulus coating thickness t_(s) is less than about 10 microns,which is a consequence of a decrease in the rigidity of the outercoating. The fiber attenuation in the absence of any microbendingattenuation penalty is assumed to be approximately 0.19 dB.km, so thenet attenuation of the coated optical fiber system is 0.19 dB/km plusthe microbend attenuation penalty.

The inventors have found that if the coating is below a certainthickness, as described herein, microbending losses can be reduced. Asshown in FIG. 11 , when the thickness of the polymer coating issufficiently reduced, an anti-resonant effect occurs in the coatinglayer, which makes the light not guided in the coating layer. Thisanti-resonant effect reduces significantly the absorption by the coatinglayer, thus decreasing the microbending loss. A conventional coatingthickness of greater than 37 microns is too large for the anti-resonanteffect. To produce this anti-resonant effect, the total thickness of thepolymer coating is less than microns, more preferably less than 20microns, and even more preferably less than 10 microns. In someembodiments, the total thickness of the polymer coating is about 2microns to about 25 microns, or about 2 microns to about 20 microns, orabout 2 microns to about 15 microns, or about 2 microns to about 10microns, or about 2 microns to about 5 microns.

As used herein the term “puncture load” refers to the amount forceimpinging on the coating of the fiber described herein. As used hereinthe term “puncture resistance” refers to the force from the fibercoating opposing the puncture load. As described further below, thecoating will rupture when the puncture load exceeds the maximum punctureresistance of the coating. With respect to puncture resistance, theanalysis by Glaesemann and Clark in the article “Quantifying thePuncture Resistance of Optical Fiber Coatings,” Proc. 52nd IWCS, pp.237-245 (1993) for fibers with one type of coating indicated that thepuncture resistance has a linear dependence on the cross-sectional areaA s of the high-modulus coating. The analysis in this paper hypothesizedthat the puncture resistance was due to hoop stress on the high-moduluscoating, which they modeled as a thin cylinder that is subjected tointernal pressure from the low-modulus inner coating. However, for mostoptical fibers, the ratio of the thickness t_(s) of the high-moduluscoating to the outer radius r₆ of is on the order of 10%, so thelow-modulus coating of the fiber can be approximated as a thick-walledcylinder with pressure P_(o) acting from the outside and exerting apuncture load. In the limit where the external pressure is much greaterthan the internal pressure from the low-modulus inner coating, themaximum hoop stress is

${\sigma_{\theta} = {\frac{{- 2}R_{s}^{2}P_{o}}{\left( {R_{s}^{2} - R_{p}^{2}} \right)} = \frac{{- 2}\pi R_{s}^{2}P_{o}}{A_{s}}}},$

where A_(S) is the cross-sectional area of the high-modulus coating.This hoop stress has the observed inverse dependence on A_(S), and thepuncture resistance is then P_(R)=P₀+C₁E_(s)A_(s), where E_(s) is themodulus of the high-modulus coating, and coefficients P₀ and C₁ havevalues of about 11.3 g and 2.1 g/MPa/mm², respectively.

Coating Examples—Preparation and Measurement Techniques

The properties of the optional low-modulus inner coating andhigh-modulus coating, as disclosed herein, were determined using themeasurement techniques described below:

Tensile Properties. The curable high-modulus coating compositions werecured and configured in the form of cured rod samples for measurement ofYoung's modulus, tensile strength at yield, yield strength, andelongation at yield. The cured rods were prepared by injecting thecurable high-modulus coating composition into Teflon® tubing having aninner diameter of about 0.025″. The rod samples were cured using aFusion D bulb at a dose of about 2.4 J/cm² (measured over a wavelengthrange of 225-424 nm by a Light Bug model IL390 from InternationalLight). After curing, the Teflon® tubing was stripped away to provide acured rod sample of the high-modulus coating composition. The cured rodswere allowed to condition for 18-24 hours at 23° C. and 50% relativehumidity before testing. Young's modulus, tensile strength at break,yield strength, and elongation at yield were measured using a SintechMTS Tensile Tester on defect-free rod samples with a gauge length of 51mm, and a test speed of 250 mm/min. Tensile properties were measuredaccording to ASTM Standard D882-97. The properties were determined as anaverage of at least five samples, with defective samples being excludedfrom the average.

In Situ Glass Transition Temperature. In situ T_(g) measurements wereperformed on fiber tube-off samples obtained from fibers having alow-modulus inner coating surrounded by a high-modulus coating. Thecoated fibers included a glass fiber having a diameter of 125 microns, alow-modulus inner coating with thickness 32.5 microns surrounding and indirect contact with the glass fiber, and a high-modulus coating withthickness 26.0 microns surrounding and in direct contact with the glassfiber. The glass fiber and low-modulus inner coating were the same forall samples measured. The low-modulus inner coating was formed from thereference low-modulus inner coating composition described below. Sampleswith a comparative high-modulus coating and a high-modulus coating inaccordance with the present disclosure were measured.

The fiber tube-off samples were obtained using the following procedure:a 0.0055″ Miller stripper was clamped down approximately 1 inch from theend of the coated fiber. The one-inch region of fiber was plunged into astream of liquid nitrogen and held in the liquid nitrogen for 3 seconds.The coated fiber was then removed from the stream of liquid nitrogen andquickly stripped to remove the coating. The stripped end of the fiberwas inspected for residual coating. If residual coating remained on theglass fiber, the sample was discarded, and a new sample was prepared.The result of the stripping process was a clean glass fiber and a hollowtube of stripped coating that includes the intact low-modulus innercoating and the high-modulus coating. The hollow tube is referred to asa “tube-off sample”. The diameters of the glass, low-modulus innercoating and high-modulus coating were measured from the end-face of theunstripped fiber.

In-situ Tg of the tube-off samples was run using a Rheometrics DMTA IVtest instrument at a sample gauge length of 9 to 10 mm. The width,thickness, and length of the tube-off sample were input to the operatingprogram of the test instrument. The tube-off sample was mounted and thencooled to approximately −85° C. Once stable, the temperature ramp wasrun using the following parameters:

Frequency: 1 Hz Strain: 0.3% Heating Rate: 2° C./min. Final Temperature:150° C. Initial Static Force =20.0 g Static >Dynamic Force by=10.0%

The in-situ Tg of a coating is defined as the maximum value of tan δ ina plot of tan δ as a function of temperature, where tan δ is defined as:

tan δ=E″/E′ and E″ is the loss modulus, which is proportional to theloss of energy as heat in a cycle of deformation and E′ is the storageor elastic modulus, which is proportional to the energy stored in acycle of deformation.

The tube-off samples exhibited distinct maxima in the tan δ plot for thelow-modulus inner coating and high-modulus coating. The maximum at lowertemperature (about −50° C.) corresponded to the in-situ Tg for thelow-modulus inner coating and the maximum at higher temperature (above50° C.) corresponded to the in-situ Tg for the high-modulus coating.

In Situ Modulus of Low-Modulus Inner Coating. In embodiments thatinclude this optional coating layer, the in situ modulus was measuredusing the following procedure. A six-inch sample of fiber was obtainedand a one-inch section from the center of the fiber was window-strippedand wiped with isopropyl alcohol. The window-stripped fiber was mountedon a sample holder/alignment stage equipped with 10 mm×5 mm rectangularaluminium tabs that were used to affix the fiber. Two tabs were orientedhorizontally and positioned so that the short 5 mm sides were facingeach other and separated by a 5 mm gap. The window-stripped fiber waslaid horizontally on the sample holder across the tabs and over the gapseparating the tabs. The coated end of one side of the window-strippedregion of the fiber was positioned on one tab and extended halfway intothe 5 mm gap between the tabs. The one-inch window-stripped regionextended over the remaining half of the gap and across the opposing tab.After alignment, the sample was removed, and a small dot of glue wasapplied to the half of each tab closest to the 5 mm gap. The fiber wasthen returned to position and the alignment stage was raised until theglue just touched the fiber. The coated end was then pulled away fromthe gap and through the glue such that the majority of the 5 mm gapbetween the tabs was occupied by the window-stripped region of thefiber. The portion of the window-stripped region remaining on theopposing tab was in contact with the glue. The very tip of the coatedend was left to extend beyond the tab and into the gap between the tabs.This portion of the coated end was not embedded in the glue and was theobject of the in situ modulus measurement. The glue was allowed to drywith the fiber sample in this configuration to affix the fiber to thetabs. After drying, the length of fiber fixed to each of the tabs wastrimmed to 5 mm. The coated length embedded in glue, the non-embeddedcoated length (the portion extending into the gap between the tabs), andthe primary diameter were measured.

The in situ modulus measurements were performed on a Rheometrics DMTA IVdynamic mechanical testing apparatus at a constant strain of 9e-6 1/sfor a time of forty-five minutes at room temperature (21° C.). The gaugelength was 15 mm. Force and the change in length were recorded and usedto calculate the in situ modulus of the low-modulus coating. Thetab-mounted fiber samples were prepared by removing any epoxy from thetabs that would interfere with the 15 mm clamping length of the testingapparatus to ensure that there was no contact of the clamps with thefiber and that the sample was secured squarely to the clamps. Theinstrument force was zeroed out. The tab to which the non-coated end ofthe fiber was affixed was then mounted to the lower clamp (measurementprobe) of the testing apparatus and the tab to which the coated end ofthe fiber was affixed was mounted to the upper (fixed) clamp of thetesting apparatus. The test was then executed, and the sample wasremoved once the analysis was completed.

In Situ Modulus of the High-Modulus Coating. For the high-moduluscoating, the in situ modulus was measured using fiber tube-off samplesprepared from the fiber samples. A 0.0055 inch Miller stripper wasclamped down approximately 1 inch from the end of the fiber sample. Thisone-inch region of fiber sample was immersed into a stream of liquidnitrogen and held for 3 seconds. The fiber sample was then removed andquickly stripped. The stripped end of the fiber sample was theninspected. If coating remained on the glass portion of the fiber sample,the tube-off sample was deemed defective and a new tube-off sample wasprepared. A proper tube-off sample is one that stripped clean from theglass and consists of a hollow tube with a low-modulus inner coating andthe high-modulus coating. The diameters of the glass, the low-modulusinner coating, and the high-modulus coating were measured from theend-face of the unstripped fiber sample.

The fiber tube-off samples were run using a Rheometrics DMTA IVinstrument at a sample gauge length 11 mm to obtain the in situ modulusof the high-modulus coating. The width, thickness, and length weredetermined and provided as input to the operating software of theinstrument. The sample was mounted and run using a time sweep program atambient temperature (21° C.) using the following parameters:

Frequency: 1 Rad/sec Strain: 0.3% Total Time=120 sec. Time PerMeasurement=1 sec Initial Static Force=15.0 g Static>Dynamic Forceby=10.0% Once completed, the last five E′ (storage modulus) data pointswere averaged. Each sample was run three times (fresh sample for eachrun) for a total of fifteen data points. The averaged value of the threeruns was reported.

Puncture Resistance of the High-Modulus Coating. Puncture resistancemeasurements were made on samples that included a glass fiber, and alow-modulus inner coating surrounded by a high-modulus coating. Theglass fiber had a cladding diameter of 125 microns. The low-modulusinner coating was formed from the reference low-modulus inner coatingcomposition listed in Table 1 below. Samples with various high-moduluscoatings were prepared as described below. The thicknesses of thelow-modulus inner coating and high-modulus coating were adjusted to varythe cross-sectional area of the high-modulus coating as described below.The ratio of the thickness of the high-modulus coating to the thicknessof the low-modulus inner coating was maintained at about 0.8 for allsamples.

The puncture resistance was measured using the technique described inthe article entitled “Quantifying the Puncture Resistance of OpticalFiber Coatings”, by G. Scott Glaesemann and Donald A. Clark, publishedin the Proceedings of the 52^(nd) International Wire & Cable Symposium,pp. 237-245 (2003), which incorporated by reference herein. A summary ofthe method is provided here. The method is an indentation method. A4-centimeter length of optical fiber was placed on a 3 mm-thick glassslide. One end of the optical fiber was attached to a device thatpermitted rotation of the optical fiber in a controlled fashion. Theoptical fiber was examined in transmission under 100× magnification androtated until the thickness of the high-modulus coating was equivalenton both sides of the glass fiber in a direction parallel to the glassslide. In this position, the thickness of the high-modulus coating wasequal on both sides of the optical fiber in a direction parallel to theglass slide. The thickness of the high-modulus coating in the directionsnormal to the glass slide and above or below the glass fiber differedfrom the thickness of the high-modulus coating in the direction parallelto the glass slide. One of the thicknesses in the direction normal tothe glass slide was greater and the other of the thicknesses in thedirection normal to the glass slide was less than the thickness in thedirection parallel to the glass slide. This position of the opticalfiber was fixed by taping the optical fiber to the glass slide at bothends and is the position of the optical fiber used for the indentationtest.

Indentation was carried out using a universal testing machine (Instronmodel 5500R or equivalent). An inverted microscope was placed beneaththe crosshead of the testing machine. The objective of the microscopewas positioned directly beneath a Vickers diamond wedge indenter, withan included angle of 75°, that was installed in the testing machine. Theglass slide with taped fiber was placed on the microscope stage andpositioned directly beneath the indenter such that the width of theindenter wedge was orthogonal to the direction of the optical fiber.With the optical fiber in place, the diamond wedge was lowered until itcontacted the surface of the high-modulus coating. The diamond wedge wasthen driven into the high-modulus coating at a rate of 0.1 mm/min andthe load on the high-modulus coating was measured. The load on thehigh-modulus coating increased as the diamond wedge was driven deeperinto the high-modulus coating until puncture occurred, at which point aprecipitous decrease in load was observed. The indentation load at whichpuncture was observed was recorded and is reported herein as grams offorce (g) and referred to herein as “puncture load”. The experiment wasrepeated with the optical fiber in the same orientation to obtain tenmeasurement points, which were averaged to determine a puncture load forthe orientation. A second set of ten measurement points was taken byrotating the orientation of the optical fiber by 180°.

Macrobending Loss. Macrobending loss was determined using the mandrelwrap test specified in standard IEC 60793-1-47. In the mandrel wraptest, the fiber is wrapped one or more times around a cylindricalmandrel having a specified diameter, and the increase in attenuation ata specified wavelength due to the bending is determined. Attenuation inthe mandrel wrap test is expressed in units of dB/turn, where one turnrefers to one revolution of the fiber about the the mandrel.Macrobending losses at a wavelength of 1310 nm, 1550 nm and 1625 nm weredetermined for selected examples described below with the mandrel wraptest using mandrels with diameters of 10 mm, 15 mm and 20 mm.

Exemplary Embodiments of Optical Fibers with Low Modulus Inner CoatingsSurrounded by High-Modulus Coatings

The specific properties of the optional low-modulus inner coating 56 andhigh-modulus coating 58 may be tailored to provide sufficient robustnessand good microbending performance for the smaller diameter fibersdisclosed herein. For example, low-modulus inner coating 56 may have alow Young's modulus and/or a low in situ modulus. The Young's modulus ofthe low-modulus inner coating is less than or equal to about 0.7 MPa, orless than or equal to about 0.6 MPa, or less than or equal to 0.5 aboutMPa, or less than or equal to about 0.4 MPa, or in the range from about0.1 MPa to about 0.7 MPa, or in the range from about 0.1 MPa to about0.4 MPa. The in situ modulus of the low-modulus inner coating is lessthan or equal to about 0.50 MPa, or less than or equal to about 0.30MPa, or less than or equal to about 0.25 MPa, or less than or equal toabout 0.20 MPa, or less than or equal to about 0.15 MPa, or less than orequal to about 0.10 MPa, or in the range from about 0.05 MPa to about0.25 MPa, or in the range from about 0.10 MPa to about 0.20 MPa.

Low-modulus inner coating 56 preferably has a higher refractive indexthan cladding region 50 of the glass fiber in order to allow it to striperrant optical signals away from core region 48. Low-modulus innercoating 56 should maintain adequate adhesion to the glass fiber duringthermal and hydrolytic aging, yet still be strippable from the glassfiber for splicing purposes.

To facilitate smaller diameter optical fibers, the low-modulus innercoating may be absent or have a smaller thickness than the low-modulusinner coating used in conventional optical fibers. The high-moduluscoating 58 may have a smaller thickness and a smaller cross-sectionalarea compared to conventional optical fibers. However, high-moduluscoating 58 must still maintain the required robustness and punctureresistance needed for high reliability in undersea cables and repeaters.As the thickness of the high-modulus coating decreases, its protectivefunction diminishes. Puncture resistance is a measure of the protectivefunction of the cross-sectional area of the outer coatings, whichinclude the high-modulus coating and the optional pigmented outercoating. A high-modulus coating with a higher puncture resistancewithstands higher abrasive pressures without failing and provides betterprotection for the glass fiber.

In order to provide the required robustness and puncture resistance,high-modulus coating 58 may have an in situ modulus greater than about1500 MPa, or greater than about 1600 MPa, or greater than about 1800MPa, or greater than about 2200 MPa, or greater than about 2500 MPa, orgreater than about 2600 MPa, or greater than about 2700 MPa, or in therange from about 1500 MPa to about 3000 MPa, or in the range from about1800 MPa to about 2800 MPa, or in the range from about 2000 MPa to about2800 MPa, or in the range from about 2400 MPa to about 2800 MPa.

In order to further provide the required robustness and punctureresistance, the product of the cross-sectional area and the in situmodulus of the high-modulus coating 58 may be greater than about 10 N,greater than about 12.5 N, greater than about 15 N, greater than about20 N, greater than about 25 N, greater than about 30 N, or in the rangefrom about 10 N to 30 N, or in the range from about 15 N to about 30 N,or in the range from about 20 N to about 30 N, or in the range fromabout 25 N to about 30 N.

In order to provide the required combination of low good microbendingperformance and puncture resistance, the ratio of the in situ modulus ofthe high-modulus coating 58 to the in situ modulus of the low-moduluscoating 56 may be greater than about 4000, or greater than about 5000,or greater than about 6000, or greater than about 7000, or greater thanabout 8000, or greater than about 9000, or greater than about 10,000, orin the range from about 4000 to about 10,000, or in the range from about4000 to about 10,000, or in the range from about 5000 to about 10,000,or in the range from about 6000 to about 10,000, or in the range fromabout 7000 to about 10,000, or in the range from about 8000 to about10,000.

Low-modulus and high-modulus coatings are typically formed by applying acurable coating composition to the glass fiber as a viscous liquid andcuring. The optical fiber may also include a pigmented outer coatingthat surrounds the high-modulus coating. The pigmented outer coating mayinclude coloring agents to mark the optical fiber for identificationpurposes and typically has a Young's modulus similar to the Young'smodulus of the high-modulus coating.

High-modulus coating 58 may be comprised of a trifunctional monomer. Aglass transition temperature (Tg) of high-modulus coating 58 may begreater than about 50° C., or greater than about 60° C., or greater thanabout 70° C., or greater than about 80° C., or greater than about 90°C., or greater than about 100° C.

Suitable low-modulus inner coatings 56 and high-modulus coatings 58 maybe used so that optical fiber 46 has a puncture resistance greater thanor equal to about 28 g, or greater than or equal to about 30 g, orgreater than or equal to about 32 g, or greater than or equal to about34 g, or greater than or equal to about 36 g, or greater than or equalto about 38 g, or greater than or equal to about 40 g, when thecross-sectional area of the high-modulus coating is less than about10,000 microns².

Suitable low-modulus inner coatings 56 and high-modulus coatings 58 maybe used so that optical fiber 46 has a puncture resistance greater thanor equal to about 22 g, or greater than or equal to about 24 g, orgreater than or equal to about 26 g, or greater than or equal to about28 g, or greater than or equal to about 30 g, when the cross-sectionalarea of the high-modulus coating is less than about 8,000 microns².

FIG. 19 depicts the microbend attenuation penalty (MAP) versus thelow-modulus inner coating thickness for fibers having step-index andtrench-assisted profiles (e.g. as shown in Table 2 above), a claddingdiameter of 100 microns, a high-modulus coating having a modulus of 1200MPa and an outer radius of 82.5 microns, and a low-modulus inner coatinghaving a modulus of 0.5 MPa. As shown in FIG. 19 and Table 7a, a MAPless than 0.1 dB/km can be achieved when the fiber has a trench-assistedprofile, a cladding diameter of about 100 microns, and the thickness ofthe low-modulus inner coating is between about 10 microns and about 26microns. The calculations were also performed on fibers havingstep-index and trench-assisted profiles, a cladding diameter of 125microns, a high-modulus coating having a modulus of 1200 MPa and anouter radius of 82.5 microns, and a low-modulus inner coating having amodulus of 0.5 MPa. As illustrated by Table 7b, a MAP less than 0.1dB/km can be achieved when the fiber has a trench-assisted profile, acladding diameter of about 125 microns, and the thickness of thelow-modulus inner coating is between about 8 microns and about 17microns.

TABLE 7a (MAP for fibers having step-index and trench-assisted profileswith a cladding diameter of 100 microns, Ep = 0.5 MPa and Es = 1200 MPa)Low- modulus Low- High- MAP MAP Inner modulus High- modulus of of GlassCoating Inner modulus Coating Step- Trench- Radius, Thick- CoatingCoating Thick- index assisted R_g ness, Radius, Radius, ness, profileprofile (mi- t_p R_p R_s t_s (dB/ (dB/ crons) (microns) (microns)(microns) (microns) km) km) 50 5 55 82.5 27.5 0.522 0.261 50 6 56 82.526.5 0.382 0.191 50 7 57 82.5 25.5 0.297 0.148 50 8 58 82.5 24.5 0.2410.120 50 9 59 82.5 23.5 0.202 0.101 50 10 60 82.5 22.5 0.174 0.087 50 1161 82.5 21.5 0.154 0.077 50 12 62 82.5 20.5 0.139 0.069 50 13 63 82.519.5 0.128 0.064 50 14 64 82.5 18.5 0.119 0.059 50 15 65 82.5 17.5 0.1130.056 50 16 66 82.5 16.5 0.108 0.054 50 17 67 82.5 15.5 0.105 0.053 5018 68 82.5 14.5 0.104 0.052 50 19 69 82.5 13.5 0.104 0.052 50 20 70 82.512.5 0.105 0.052 50 21 71 82.5 11.5 0.108 0.054 50 22 72 82.5 10.5 0.1120.056 50 23 73 82.5 9.5 0.118 0.059 50 24 74 82.5 8.5 0.126 0.063 50 2575 82.5 7.5 0.137 0.069 50 26 76 82.5 6.5 0.151 0.075 50 27 77 82.5 5.50.168 0.084 50 28 78 82.5 4.5 0.189 0.094 50 29 79 82.5 3.5 0.216 0.10850 30 80 82.5 2.5 0.256 0.128 50 31 81 82.5 1.5 0.333 0.166

TABLE 7b (MAP for fibers having step-index and trench-assisted profileswith cladding diameters of 125 microns, Ep = 0.5 MPa and Es = 1200 MPa)Low- modulus Low- High- MAP MAP Inner modulus High- modulus of of GlassCoating Inner modulus Coating Step- Trench- Radius, Thick- CoatingCoating Thick- index assisted R_g ness, Radius, Radius, ness, profileprofile (mi- t_p R_p R_s t_s (dB/ (dB/ crons) (microns) (microns)(microns) (microns) km) km) 62.5 5 67.5 82.5 15 0.335 0.167 62.5 6 68.582.5 14 0.258 0.129 62.5 7 69.5 82.5 13 0.212 0.106 62.5 8 70.5 82.5 120.183 0.091 62.5 9 71.5 82.5 11 0.164 0.082 62.5 10 72.5 82.5 10 0.1520.076 62.5 11 73.5 82.5 9 0.146 0.073 62.5 12 74.5 82.5 8 0.143 0.07262.5 13 75.5 82.5 7 0.145 0.072 62.5 14 76.5 82.5 6 0.149 0.075 62.5 1577.5 82.5 5 0.157 0.078 62.5 16 78.5 82.5 4 0.168 0.084 62.5 17 79.582.5 3 0.185 0.092 62.5 18 80.5 82.5 2 0.216 0.108 62.5 19 81.5 82.5 10.299 0.149

FIG. 20 depicts the MAP versus the thickness of the low-modulus innercoating for fibers having trench-assisted fiber profiles (e.g. as shownin Table 2 above), a cladding diameter of 100 microns, a low-modulusinner coating having a modulus of 0.5 MPa and a high-modulus coatingshaving moduli of 1.2, 1.6 and 2.0 GPa. As shown in FIG. 20 and Table 8a,a MAP less than 0.1 dB/km can be achieved when the high-modulus coatinghas a modulus of 1.6 GPa and the thickness of the low-modulus innercoating is between about 8 and about 29 microns. A MAP less than 0.05dB/km can be achieved when the high-modulus coating has a modulus of 1.6GPa and the thickness of the low-modulus inner coating is between about13 and about 24 microns. A MAP less than 0.1 dB/km can be achieved whenthe high-modulus coating has a modulus of 2.0 GPa and the thickness ofthe low-modulus inner coating is between about 7 and about 30 microns. AMAP less than 0.05 dB/km can be achieved when the high-modulus coatinghas a modulus of 2.0 GPa and the thickness of the low-modulus innercoating is between about 11 and about 26 microns. The calculations werealso performed on fibers having trench-assisted profiles, a claddingdiameter of 125 microns, a low-modulus inner coating having a modulus of0.5 MPa and high-modulus coatings having moduli of 1.2, 1.6 and 2.0 GPa.As shown in Table 8b, a MAP less than 0.1 dB/km can be achieved when thehigh-modulus coating has a modulus of 1.6 GPa and the thickness of thelow-modulus inner coating is between about 6 and about 18 microns. A MAPless than 0.06 dB/km can be achieved when the high-modulus coating has amodulus of 1.6 GPa and the thickness of the low-modulus inner coating isbetween about 10 and about 14 microns. A MAP less than 0.1 dB/km can beachieved when the high-modulus coating has a modulus of 2.0 GPa and thethickness of the low-modulus inner coating is between about 6 and about18 microns. A MAP less than 0.05 dB/km can be achieved when thehigh-modulus coating has a modulus of 2.0 GPa and the thickness of thelow-modulus inner coating is between about 10 and about 14 microns.

TABLE 8a (MAP for fibers having trench-assisted profiles with a claddingdiameter of 100 microns and Ep = 0.5 MPa) Low-modulus Low-modulusHigh-modulus High-modulus MAP for MAP for MAP for Inner Coating InnerCoating Coating Coating Es = 1.2 Es = 1.6 Es = 2.0 Glass Radius,Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s GPa GPa GPa R_g(microns) (microns) (microns) (microns) (microns) (dB/km) (dB/km)(dB/km) 50 5 55 82.5 27.5 0.261 0.196 0.157 50 6 56 82.5 26.5 0.1910.144 0.115 50 7 57 82.5 25.5 0.148 0.111 0.089 50 8 58 82.5 24.5 0.1200.090 0.072 50 9 59 82.5 23.5 0.101 0.076 0.061 50 10 60 82.5 22.5 0.0870.066 0.052 50 11 61 82.5 21.5 0.077 0.058 0.046 50 12 62 82.5 20.50.069 0.052 0.042 50 13 63 82.5 19.5 0.064 0.048 0.038 50 14 64 82.518.5 0.059 0.045 0.036 50 15 65 82.5 17.5 0.056 0.042 0.034 50 16 6682.5 16.5 0.054 0.041 0.033 50 17 67 82.5 15.5 0.053 0.040 0.032 50 1868 82.5 14.5 0.052 0.039 0.031 50 19 69 82.5 13.5 0.052 0.039 0.032 5020 70 82.5 12.5 0.052 0.040 0.032 50 21 71 82.5 11.5 0.054 0.041 0.03350 22 72 82.5 10.5 0.056 0.043 0.034 50 23 73 82.5 9.5 0.059 0.045 0.03750 24 74 82.5 8.5 0.063 0.049 0.040 50 25 75 82.5 7.5 0.069 0.053 0.04450 26 76 82.5 6.5 0.075 0.059 0.049 50 27 77 82.5 5.5 0.084 0.067 0.05650 28 78 82.5 4.5 0.094 0.076 0.064 50 29 79 82.5 3.5 0.108 0.089 0.07650 30 80 82.5 2.5 0.128 0.106 0.092 50 31 81 82.5 1.5 0.166 0.139 0.121

TABLE 8b (MAP for fibers having trench-assisted profiles with a claddingdiameter of 125 microns and Ep = 0.5 MPa Low-modulus Low-modulusHigh-modulus High-modulus MAP for MAP for MAP for Inner Coating InnerCoating Coating Coating Es = 1.2 Es = 1.6 Es = 2.0 Glass Radius,Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s GPa GPa GPa R_g(microns) (microns) (microns) (microns) (microns) (dB/km) (dB/km)(dB/km) 62.5 5 67.5 82.5 15 0.167 0.126 0.101 62.5 6 68.5 82.5 14 0.1290.097 0.078 62.5 7 69.5 82.5 13 0.106 0.080 0.064 62.5 8 70.5 82.5 120.091 0.069 0.056 62.5 9 71.5 82.5 11 0.082 0.062 0.050 62.5 10 72.582.5 10 0.076 0.058 0.047 62.5 11 73.5 82.5 9 0.073 0.056 0.045 62.5 1274.5 82.5 8 0.072 0.055 0.045 62.5 13 75.5 82.5 7 0.072 0.056 0.046 62.514 76.5 82.5 6 0.075 0.059 0.049 62.5 15 77.5 82.5 5 0.078 0.063 0.05362.5 16 78.5 82.5 4 0.084 0.068 0.058 62.5 17 79.5 82.5 3 0.092 0.0760.065 63.5 18 81.5 83.5 2 0.108 0.090 0.078 64.5 19 83.5 84.5 1 0.1490.125 0.108

FIG. 21 depicts the puncture resistance versus the thickness of thelow-modulus inner coating for fibers having a trench-assisted profile(e.g. as shown in Table 2 above), a cladding diameter of 100 microns, alow-modulus coating having a modulus of 0.5 MPa and a high-moduluscoatings having moduli of 1.2, 1.6 and 2.0 GPa. As shown in FIG. 21 andTable 9a, a puncture resistance greater than 30 g can be achieved whenthe high-modulus coating has a modulus of 1.6 GPa and the thickness ofthe low-modulus inner coating is less than about 14 microns. A punctureresistance greater than 35 g can be achieved when the high-moduluscoating has a modulus of 1.6 GPa and the thickness of the low-modulusinner coating is less than about 8 microns. A puncture resistancegreater than 30 g can be achieved when the high-modulus coating has amodulus of 2.0 GPa and the thickness of the low-modulus inner coating isless than about 18 microns. A puncture resistance greater than 35 g canbe achieved when the high-modulus coating has a modulus of 2.0 GPa andthe thickness of the low-modulus inner coating is less than about 14microns. A puncture resistance greater than 40 g can be achieved whenthe high-modulus coating has a modulus of 2.0 GPa and the thickness ofthe low-modulus inner coating is less than about 9 microns. Thecalculations were also performed on fibers having a trench-assistedprofile, a cladding diameter of 125 microns, a low-modulus inner coatinghaving a modulus of 0.5 MPa and high-modulus coatings having moduli of1.2, 1.6 and 2.0 GPa. As shown in Table 9b, a puncture resistancegreater than 20 g can be achieved when the high-modulus coating has amodulus of 1.6 GPa and the thickness of the low-modulus inner coating isless than about 12 microns. A puncture resistance greater than 25 g canbe achieved when the high-modulus coating has a modulus of 1.6 GPa andthe thickness of the low-modulus inner coating is less than about 7microns. A puncture resistance greater than 20 g can be achieved whenthe high-modulus coating has a modulus of 2.0 GPa and the thickness ofthe low-modulus inner coating is less than about 13 microns. A punctureresistance greater than 25 g can be achieved when the high-moduluscoating has a modulus of 2.0 GPa and the thickness of the low-modulusinner coating is less than about 9 microns. A puncture resistancegreater than 30 g can be achieved when the high-modulus coating has amodulus of 2.0 GPa and the thickness of the low-modulus inner coating isless than or equal to about 6 microns.

TABLE 9a (Puncture resistance for fibers having trench-assisted profileswith a cladding diameter of 100 microns and Ep = 0.5 MPa) Low-modulusLow-modulus High-modulus High-modulus Puncture Puncture Puncture InnerCoating Inner Coating Coating Coating Resistance Resistance ResistanceGlass Radius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s forEs = 1.2 for Es = 1.6 for Es = 2.0 R_g (microns) (microns) (microns)(microns) (microns) GPa (g) GPa (g) GPa (g) 50 5 55 82.5 27.5 31.2 37.944.5 50 6 56 82.5 26.5 30.6 37.1 43.5 50 7 57 82.5 25.5 30.0 36.3 42.550 8 58 82.5 24.5 29.4 35.5 41.5 50 9 59 82.5 23.5 28.8 34.7 40.5 50 1060 82.5 22.5 28.2 33.8 39.5 50 11 61 82.5 21.5 27.5 33.0 38.4 50 12 6282.5 20.5 26.9 32.1 37.3 50 13 63 82.5 19.5 26.2 31.2 36.2 50 14 64 82.518.5 25.6 30.3 35.1 50 15 65 82.5 17.5 24.9 29.4 34.0 50 16 66 82.5 16.524.2 28.5 32.8 50 17 67 82.5 15.5 23.5 27.6 31.6 50 18 68 82.5 14.5 22.826.6 30.5 50 19 69 82.5 13.5 22.0 25.6 29.2 50 20 70 82.5 12.5 21.3 24.728.0 50 21 71 82.5 11.5 20.6 23.7 26.8 50 22 72 82.5 10.5 19.8 22.7 25.550 23 73 82.5 9.5 19.1 21.7 24.2 50 24 74 82.5 8.5 18.3 20.6 23.0 50 2575 82.5 7.5 17.5 19.6 21.6 50 26 76 82.5 6.5 16.7 18.5 20.3 50 27 7782.5 5.5 15.9 17.4 19.0 50 28 78 82.5 4.5 15.1 16.3 17.6 50 29 79 82.53.5 14.2 15.2 16.2 50 30 80 82.5 2.5 13.4 14.1 14.8 50 31 81 82.5 1.512.5 13.0 13.4

TABLE 9b (Puncture resistance for fibers having trench-assisted profileswith a cladding diameter of 100 microns and Ep = 0.5 MPa) Low-modulusLow-modulus High-modulus High-modulus Puncture Puncture Puncture InnerCoating Inner Coating Coating Coating Resistance Resistance ResistanceGlass Radius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s forEs = 1.2 for Es = 1.6 for Es = 2.0 R_g (microns) (microns) (microns)(microns) (microns) GPa (g) GPa (g) GPa (g) 62.5 5 67.5 82.5 15 23.127.1 31.0 62.5 6 68.5 82.5 14 22.4 26.1 29.9 62.5 7 69.5 82.5 13 21.725.2 28.6 62.5 8 70.5 82.5 12 20.9 24.2 27.4 62.5 9 71.5 82.5 11 20.223.2 26.2 62.5 10 72.5 82.5 10 19.4 22.2 24.9 62.5 11 73.5 82.5 9 18.721.1 23.6 62.5 12 74.5 82.5 8 17.9 20.1 22.3 62.5 13 75.5 82.5 7 17.119.0 21.0 62.5 14 76.5 82.5 6 16.3 18.0 19.6 62.5 15 77.5 82.5 5 15.516.9 18.3 62.5 16 78.5 82.5 4 14.7 15.8 16.9 62.5 17 79.5 82.5 3 13.814.7 15.5 63.5 18 81.5 83.5 2 13.0 13.5 14.1 64.5 19 83.5 84.5 1 12.112.4 12.7

FIG. 22 depicts the MAP versus the thickness of the low-modulus innercoating for fibers having a trench-assisted fiber profile (e.g. as shownin Table 2 above), a cladding diameter of 100 microns, a high-moduluscoating having a modulus of 1.6 GPa and low-modulus inner coatingshaving moduli of 0.5, 0.35 and 0.2 MPa. As shown in FIG. 22 and Table10a, a MAP less than 0.05 dB/km can be achieved when the low-modulusinner coating has a modulus of 0.35 MPa and the thickness of thelow-modulus inner coating is between about 8 and about 29 microns. A MAPless than 0.02 dB/km can be achieved when the low-modulus inner coatinghas a modulus of 0.35 MPa and the thickness of the low-modulus innercoating is between about 16 and about 21 microns. A MAP less than 0.05dB/km can be achieved when the low-modulus inner coating has a modulusof 0.2 MPa and the thickness of the low-modulus inner coating is betweenabout 4 and about 31 microns. A MAP less than 0.02 dB/km can be achievedwhen the low-modulus inner coating has a modulus of 0.2 MPa and thethickness of the low-modulus inner coating is between about 7 and about29 microns. A MAP less than 0.01 dB/km can be achieved when thelow-modulus inner coating has a modulus of 0.2 MPa and the thickness ofthe low-modulus inner coating is between about 11 and about 25 microns.A MAP less than dB/km can be achieved when the low-modulus inner coatinghas a modulus of 0.2 MPa and the thickness of the low-modulus innercoating is between about 16 and about 21 microns. The calculations werealso performed on fibers having a trench-assisted fiber profile, acladding diameter of 125 microns, a high-modulus coating having amodulus of 1.6 GPa and low-modulus inner coatings having moduli of 0.5,0.35 and 0.2 MPa. As shown in Table 10b, a MAP less than 0.05 dB/km canbe achieved when the low-modulus inner coating has a modulus of 0.35 MPaand the thickness of the low-modulus inner coating is between about 6and about 18 microns. A MAP less than 0.03 dB/km can be achieved whenthe low-modulus inner coating has a modulus of 0.35 MPa and thethickness of the low-modulus inner coating is between about 10 and about14 microns. A MAP less than 0.03 dB/km can be achieved when thelow-modulus inner coating has a modulus of 0.2 MPa and the thickness ofthe low-modulus inner coating is between about 4 and about 19 microns. AMAP less than 0.02 dB/km can be achieved when the low-modulus innercoating has a modulus of 0.2 MPa and the thickness of the low-modulusinner coating is between about 6 and about 17 microns. A MAP less than0.01 dB/km can be achieved when the low-modulus inner coating has amodulus of 0.2 MPa and the thickness of the low-modulus inner coating isbetween about 10 and about 13 microns.

TABLE 10a (MAP for fibers having trench-assisted profiles with acladding diameter of 100 microns and Es = 1.6 GPa) Low-modulusLow-modulus High-modulus High-modulus MAP for MAP for MAP for InnerCoating Inner Coating Coating Coating Ep = 0.5 Ep = 0.35 Ep = 0.2 GlassRadius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s MPa MPaMPa R_g (microns) (microns) (microns) (microns) (microns) (dB/km)(dB/km) (dB/km) 50 5 55 82.5 27.5 0.196 0.096 0.031 50 6 56 82.5 26.50.144 0.070 0.023 50 7 57 82.5 25.5 0.111 0.055 0.018 50 8 58 82.5 24.50.090 0.044 0.015 50 9 59 82.5 23.5 0.076 0.037 0.012 50 10 60 82.5 22.50.066 0.032 0.011 50 11 61 82.5 21.5 0.058 0.028 0.009 50 12 62 82.520.5 0.052 0.026 0.008 50 13 63 82.5 19.5 0.048 0.024 0.008 50 14 6482.5 18.5 0.045 0.022 0.007 50 15 65 82.5 17.5 0.042 0.021 0.007 50 1666 82.5 16.5 0.041 0.020 0.007 50 17 67 82.5 15.5 0.040 0.020 0.006 5018 68 82.5 14.5 0.039 0.019 0.006 50 19 69 82.5 13.5 0.039 0.019 0.00650 20 70 82.5 12.5 0.040 0.020 0.006 50 21 71 82.5 11.5 0.041 0.0200.007 50 22 72 82.5 10.5 0.043 0.021 0.007 50 23 73 82.5 9.5 0.045 0.0230.008 50 24 74 82.5 8.5 0.049 0.024 0.008 50 25 75 82.5 7.5 0.053 0.0270.009 50 26 76 82.5 6.5 0.059 0.030 0.010 50 27 77 82.5 5.5 0.067 0.0350.012 50 28 78 82.5 4.5 0.076 0.041 0.015 50 29 79 82.5 3.5 0.089 0.0480.018 50 30 80 82.5 2.5 0.106 0.059 0.023 50 31 81 82.5 1.5 0.139 0.0780.031

TABLE 10b (MAP for fibers having trench-assisted profiles with acladding diameter of 125 microns and Es = 1.6 GPa) Low-modulusLow-modulus High-modulus High-modulus MAP for MAP for MAP for InnerCoating Inner Coating Coating Coating Ep = 0.5 Ep = 0.35 Ep = 0.2 GlassRadius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s MPa MPaMPa R_g (microns) (microns) (microns) (microns) (microns) (dB/km)(dB/km) (dB/km) 62.5 5 67.5 82.5 15 0.126 0.062 0.020 62.5 6 68.5 82.514 0.097 0.048 0.016 62.5 7 69.5 82.5 13 0.080 0.040 0.013 62.5 8 70.582.5 12 0.069 0.034 0.011 62.5 9 71.5 82.5 11 0.062 0.031 0.010 62.5 1072.5 82.5 10 0.058 0.029 0.010 62.5 11 73.5 82.5 9 0.056 0.028 0.00962.5 12 74.5 82.5 8 0.055 0.028 0.009 62.5 13 75.5 82.5 7 0.056 0.0290.010 62.5 14 76.5 82.5 6 0.059 0.030 0.011 62.5 15 77.5 82.5 5 0.0630.033 0.012 62.5 16 78.5 82.5 4 0.068 0.037 0.014 62.5 17 79.5 82.5 30.076 0.042 0.016 63.5 18 81.5 83.5 2 0.090 0.050 0.020 64.5 19 83.584.5 1 0.125 0.070 0.028

Table 1 la depicts the MAP versus the thickness of the low-modulus innercoating for fibers having a trench-assisted fiber profile (e.g. as shownin Table 2 above), a cladding diameter of 100 microns, a high-moduluscoating having a modulus of 2.0 GPa and low-modulus inner coatingshaving moduli of 0.35, 0.2 and 0.1 MPa. As shown in Table 1 la, a MAPless than 0.02 dB/km can be achieved when the low-modulus inner coatinghas a modulus of 0.35 MPa and the thickness of the low-modulus innercoating is between about 6 and about 30 microns. A MAP less than 0.02dB/km can be achieved when the low-modulus inner coating has a modulusof 0.35 MPa and the thickness of the low-modulus inner coating isbetween about 13 and about 23 microns. A MAP less than 0.02 dB/km can beachieved when the low-modulus inner coating has a modulus of 0.2 MPa andthe thickness of the low-modulus inner coating is between about 6 andabout 30 microns. A MAP less than 0.01 dB/km can be achieved when thelow-modulus inner coating has a modulus of 0.2 MPa and the thickness ofthe low-modulus inner coating is between about 9 and about 27 microns. AMAP less than 0.005 dB/km can be achieved when the low-modulus innercoating has a modulus of 0.2 MPa and the thickness of the low-modulusinner coating is between about 14 and about 22 microns. A MAP less than0.005 dB/km can be achieved when the low-modulus inner coating has amodulus of 0.1 MPa and the thickness of the low-modulus inner coating isbetween about 6 and about 29 microns. A MAP less than 0.002 dB/km can beachieved when the low-modulus inner coating has a modulus of 0.1 MPa andthe thickness of the low-modulus inner coating is between about 13 andabout 23 microns. The calculations were also performed on fibers havinga trench-assisted fiber profile, a cladding diameter of 125 microns, ahigh-modulus coating having a modulus of 2.0 GPa and low-modulus innercoatings having moduli of moduli of 0.35, 0.2 and 0.1 MPa. As shown inTable 10b, a MAP less than 0.03 dB/km can be achieved when thelow-modulus inner coating has a modulus of 0.35 MPa and the thickness ofthe low-modulus inner coating is between about 5 and about 12 microns. AMAP less than 0.02 dB/km can be achieved when the low-modulus innercoating has a modulus of 0.2 MPa and the thickness of the low-modulusinner coating is between about 5 and about 18 microns. A MAP less than0.01 dB/km can be achieved when the low-modulus inner coating has amodulus of 0.2 MPa and the thickness of the low-modulus inner coating isbetween about 8 and about 14 microns. A MAP less than 0.005 dB/km can beachieved when the low-modulus inner coating has a modulus of 0.1 MPa andthe thickness of the low-modulus inner coating is between about 5 andabout 18 microns. A MAP less than 0.01 dB/km can be achieved when thelow-modulus inner coating has a modulus of 0.1 MPa and the thickness ofthe low-modulus inner coating is between about 8 and about 14 microns.

TABLE 11a (MAP for fibers having trench-assisted profiles with acladding diameter of 100 microns and Es = 2.0 GPa) Low-modulusLow-modulus High-modulus High-modulus MAP for MAP for MAP for InnerCoating Inner Coating Coating Coating Ep = 0.35 Ep = 0.2 Ep = 0.1 GlassRadius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s MPa MPaMPa R_g (microns) (microns) (microns) (microns) (microns) (dB/km)(dB/km) (dB/km) 50 5 55 82.5 27.5 0.077 0.025 0.006 50 6 56 82.5 26.50.056 0.018 0.005 50 7 57 82.5 25.5 0.044 0.014 0.004 50 8 58 82.5 24.50.036 0.012 0.003 50 9 59 82.5 23.5 0.030 0.010 0.002 50 10 60 82.5 22.50.026 0.008 0.002 50 11 61 82.5 21.5 0.023 0.007 0.002 50 12 62 82.520.5 0.021 0.007 0.002 50 13 63 82.5 19.5 0.019 0.006 0.002 50 14 6482.5 18.5 0.018 0.006 0.001 50 15 65 82.5 17.5 0.017 0.005 0.001 50 1666 82.5 16.5 0.016 0.005 0.001 50 17 67 82.5 15.5 0.016 0.005 0.001 5018 68 82.5 14.5 0.015 0.005 0.001 50 19 69 82.5 13.5 0.016 0.005 0.00150 20 70 82.5 12.5 0.016 0.005 0.001 50 21 71 82.5 11.5 0.016 0.0050.001 50 22 72 82.5 10.5 0.017 0.006 0.001 50 23 73 82.5 9.5 0.018 0.0060.002 50 24 74 82.5 8.5 0.020 0.007 0.002 50 25 75 82.5 7.5 0.022 0.0070.002 50 26 76 82.5 6.5 0.025 0.008 0.002 50 27 77 82.5 5.5 0.029 0.0100.003 50 28 78 82.5 4.5 0.034 0.012 0.003 50 29 79 82.5 3.5 0.041 0.0150.004 50 30 80 82.5 2.5 0.051 0.020 0.006 50 31 81 82.5 1.5 0.067 0.0270.009

TABLE 11b (MAP for fibers having trench-assisted profiles with acladding diameter of 125 microns and Es = 2.0 GPA Low-modulusLow-modulus High-modulus High-modulus MAP for MAP for MAP for InnerCoating Inner Coating Coating Coating Ep = 0.35 Ep = 0.2 Ep = 0.1 GlassRadius, Thickness, t_p Radius, R_p Radius, R_s Thickness, t_s MPa MPaMPa R_g (microns) (microns) (microns) (microns) (microns) (dB/km)(dB/km) (dB/km) 62.5 5 67.5 82.5 15 0.050 0.016 0.004 62.5 6 68.5 82.514 0.039 0.013 0.003 62.5 7 69.5 82.5 13 0.032 0.010 0.003 62.5 8 70.582.5 12 0.028 0.009 0.002 62.5 9 71.5 82.5 11 0.025 0.008 0.002 62.5 1072.5 82.5 10 0.023 0.008 0.002 62.5 11 73.5 82.5 9 0.023 0.008 0.00262.5 12 74.5 82.5 8 0.023 0.008 0.002 62.5 13 75.5 82.5 7 0.024 0.0080.002 62.5 14 76.5 82.5 6 0.025 0.009 0.002 62.5 15 77.5 82.5 5 0.0280.010 0.003 62.5 16 78.5 82.5 4 0.031 0.011 0.003 62.5 17 79.5 82.5 30.036 0.014 0.004 63.5 18 81.5 83.5 2 0.043 0.017 0.005 64.5 19 83.584.5 1 0.061 0.024 0.008

The results of the calculated MAP and puncture resistance given in FIGS.19-23 and Table 7-11 can be merged to provide the minimum thicknesses ofthe low-modulus inner coating and high-modulus coating that yield amaximum MAP and minimum puncture resistance for input values of the themaximum modulus of low-modulus primary coating (Ep), the minimum modulusof the high-modulus coating (Es), the glass radius (Rg), and the radiusof the high-modulus coating (R_(S)). Table 12a summarize the coatingproperties for Examples 1-4 with cladding diameters of 100 micron andEs=1.6 GPa. Tables 12b and 12c summarize the the coating properties forExample 5-14 with cladding diameters of 100 micron and Es=2.0 GPa.Tables 12d and 12e summarize the the coating properties for Examples15-21 with cladding diameters of 100 micron.

TABLE 12a (Minimum thicknesses of the low-modulus inner coating andhigh-modulus coating that provide the given values of the maximum MAPand minimum puncture resistance). Example 1 Example 2 Example 3 Example4 Glass Radius, R_g (microns) 50 50 50 50 Maximum Ep (Mpa) 0.5 0.35 0.20.2 Minimum Es (Gpa) 1.6 1.6 1.6 1.6 Maximum MAP of Trench-assistedprofile 0.05 0.03 0.03 0.01 (dB/km) Minimum Puncture Resistance (g) 3030 30 30 Minimum Low-modulus Inner Coating 13 11 7 11 Thickness, t_p(microns) Maximum Low-modulus Inner Coating 14 14 14 14 Thickness, t_p(microns) Minimum High-modulus Coating Thickness, 18.5 18.5 18.5 18.5t_s (microns) Maximum High-modulus Coating Thickness, 19.5 21.5 25.521.5 t_s (microns) Minimum High-modulus Coating Radius, R_s 64 64 64 64(microns) Minimum Cross Sectional Area of Secondary 17029 17029 1702917029 Coating (sq. microns)

TABLE 12b (Minimum thicknesses of the low-modulus inner coating andhigh-modulus coating that provide the given values of the maximum MAPand minimum puncture resistance). Example 5 Example 6 Example 7 Example8 Example 9 Glass Radius, R_g (microns) 50 50 50 50 50 Maximum Ep (Mpa)0.5 0.35 0.5 0.35 0.2 Minimum Es (Gpa) 2 2 2 2 2 Maximum MAP ofTrench-assisted profile 0.05 0.02 0.05 0.02 0.02 (dB/km) MinimumPuncture Resistance (g) 30 30 35 35 35 Minimum Low-modulus Inner Coating11 13 11 13 6 Thickness, t_p (microns) Maximum Low-modulus Inner Coating18 18 14 14 14 Thickness, t_p (microns) Minimum High-modulus CoatingThickness, 14.5 14.5 18.5 18.5 18.5 t_s (microns) Maximum High-modulusCoating Thickness, 21.5 19.5 21.5 19.5 26.5 t_s (microns) MinimumHigh-modulus Coating Radius, R_s 68 68 64 64 64 (microns) Minimum CrossSectional Area of Secondary 13711 13711 17029 17029 17029 Coating (sq.microns)

TABLE 12c (Minimum thicknesses of the low-modulus inner coating andhigh-modulus coating that provide the given values of the maximum MAPand minimum puncture resistance). Example Example Example ExampleExample 10 11 12 13 14 Glass Radius, R_g (microns) 50 50 50 50 50Maximum Ep (Mpa) 0.2 0.2 0.1 0.2 0.1 Minimum Es (Gpa) 2 2 2 2 2 MaximumMAP of Trench-assisted profile 0.01 0.007 0.003 0.01 0.007 (dB/km)Minimum Puncture Resistance (g) 35 35 35 40 40 Minimum Low-modulus InnerCoating 9 11 9 9 5 Thickness, t_p (microns) Maximum Low-modulus InnerCoating 14 14 14 9.5 9.5 Thickness, t_p (microns) Minimum High-modulusCoating Thickness, 18.5 18.5 18.5 23 23 t_s (microns) MaximumHigh-modulus Coating Thickness, 23.5 21.5 23.5 23.5 27.5 t_s (microns)Minimum High-modulus Coating Radius, R_s 64 64 64 59.5 59.5 (microns)Minimum Cross Sectional Area of Secondary 17029 17029 17029 20521 20521Coating (sq. microns)

TABLE 12d (Minimum thicknesses of the low-modulus inner coating andhigh-modulus coatingthat provide the given values of the maximum MAP andminimum puncture resistance). Ex- Ex- Ex- Ex- ample ample ample ample 1517 18 19 Glass Radius, R_g (microns) 62.5 62.5 62.5 62.5 Maximum Ep(Mpa) 0.35 0.35 0.35 0.2 Minimum Es (Gpa) 1.6 1.6 2 2 Maximum MAP ofTrench-assisted 0.05 0.03 0.03 0.01 profile (dB/km) Minimum PunctureResistance (g) 20 20 25 25 Minimum Low-modulus Inner 6 10 8 7 CoatingThickness, t_p (microns) Maximum Low-modulus Inner 12 12 10 10 CoatingThickness, t_p (microns) Minimum High-modulus Coating 8 8 10 10Thickness, t_s (microns) Maximum High-modulus Coating 14 10 12 13Thickness, t_s (microns) Minimum High-modulus Coating 74.5 74.5 72.572.5 Radius, R_s (microns) Minimum Cross Sectional Area of 7892 78929739 9739 Secondary Coating (sq. microns)

TABLE 12e (Minimum thicknesses of the low-modulus inner coating andhigh-modulus coating that provide the given values of the maximum MAPand minimum puncture resistance). Ex- Ex- Ex- ample ample ample 20 21 22Glass Radius, R_g (microns) 62.5 62.5 62.5 Maximum Ep (Mpa) 0.1 0.1 0.1Minimum Es (Gpa) 2 2 2 Maximum MAP of Trench-assisted profile 0.0070.003 0.007 (dB/km) Minimum Puncture Resistance (g) 25 25 30 MinimumLow-modulus Inner Coating 5 7 5 Thickness, t_p (microns) MaximumLow-modulus Inner Coating 10 10 6 Thickness, t_p (microns) MinimumHigh-modulus Coating Thickness, 10 10 14 t_s (microns) MaximumHigh-modulus Coating Thickness, 15 13 15 t_s (microns) MinimumHigh-modulus Coating Radius, R_s 72.5 72.5 68.5 (microns) Minimum CrossSectional Area of Secondary 9739 9739 13283 Coating (sq. microns)

Reduced Diameter Exemplary Embodiments

As discussed above, the optical fibers of the embodiments disclosedherein may have a glass diameter of about 125 microns and a reducedcoating diameter may have an outer diameter of about 175 microns orless, or about 170 microns or less, or about 165 microns or less, orabout 160 microns or less, or about 145 microns or less. It is notedthat the outer diameter of cladding region 50 is the glass diameter ofoptical fiber 46 and that the outer diameter of high-modulus coating 58may be the outer overall diameter of optical fiber 46 (when an outerpigmented outer coating layer is not applied).

In some exemplary examples, cladding region 50 has an outer diameter ofabout 125 microns and high-modulus coating 58 has an outer diameterbetween about 155 and 175 microns, or cladding region 50 has an outerdiameter of about 125 microns and high-modulus coating 58 has an outerdiameter between about 160 and 170 microns.

As discussed above, the optical fibers of the embodiments disclosedherein may also have a glass diameter of about 100 microns and a reducedcoating diameter may have an outer diameter of about 175 microns orless, or about 170 microns or less, or about 165 microns or less, orabout 160 microns or less, or about 145 microns or less. It is notedthat the outer diameter of cladding region 50 is the glass diameter ofoptical fiber 46 and that the outer diameter of high-modulus coating 58may be the outer overall diameter of optical fiber 46 (when an outerpigmented outer coating layer is not applied).

In some exemplary examples, cladding region 50 has an outer diameter ofabout 100 microns and high-modulus coating 58 has an outer diameterbetween about 155 and 175 microns, or cladding region 50 has an outerdiameter of about 100 microns and high-modulus coating 58 has an outerdiameter between about 160 and 170 microns.

As discussed above, the reduced diameter optical fiber profile designsof the present disclosure provide particular advantages, such as, forexample, a higher fiber count in submarine cables and repeaters.However, a reduction in the cladding diameter of an optical fiber mayallow some light to leak through the cladding, due to the reducedprofile of the cladding. Thus, the off-set trench designs of the presentdisclosure have trench volumes of about 30% Δ-micron² or greater toadvantageously reduce “tunneling” or “radiation” losses caused byleaking of the light through the reduced diameter cladding.

To facilitate a decrease in the diameter of the optical fiber, it ispreferable to minimize the thickness r₅-r₄ of the low-modulus innercoating or to eliminate it entirely. The thickness r₅-r₄ of thelow-modulus coating is less than or equal to about 8.0 microns, or lessthan or equal to about 7.0 microns, or less than or equal to about 6.0microns, or less than or equal to about 5.0 microns, or in the rangefrom about 4.0 microns to about 8.0 microns, or in the range from about5.0 microns to about 7.0 microns. However, elimination or reduction inthe thickness of the low-modulus inner coating of an optical fiber willincrease microbending sensitivity. This increased sensitivity ismitigated in the disclosed design through the addition of an off-settrench with a volume greater than about 30% Δ-micron².

The radius r₆ of the high-modulus coating is less than or equal to about87.5 microns, or less than or equal to about 85.0 microns, or less thanor equal to about 82.5 microns, or less than or equal to about 80.0microns. It is also preferable to optimize the thickness r₆-r₅ of thehigh-modulus coating to balance the reduction in the diameter of thefiber with having a sufficiently high cross-sectional area for highpuncture resistance. The thickness r₆-r₅ of the high-modulus coating isless than or equal to about 25.0 microns, or less than or equal to about20.0 microns, or less than or equal to about 15.0 microns, or in therange from about 15.0 microns to about 25.0 microns, or in the rangefrom about 17.5 microns to about 22.5 microns, or in the range fromabout 18.0 microns to about 22.0 microns. The total thickness of thelow-modulus coating and the high-modulus coating is about 25 microns orless, preferably about 20 microns or less. In some embodiments, thetotal thickness of the low-modulus coating and the high-modulus coatingis about 10 microns to about 25 microns. In some embodiments, the ratioof the thickness of the low-modulus coating layer coating to thethickness of the high-modulus coating layer is in the range of 0.8 to1.2.

Thus, optical fibers in accordance with the embodiments of the presentdisclosure have reduced coating diameters compared to traditionaloptical fibers. The size reduction helps to increase the “fiber count”and fiber density within, for example, a submarine repeater or a cable.

Table 10 below shows an average coating thickness for five high-moduluscoating samples. Examples 1 and 2 compared with Examples 3, 4, and 5show that average high-modulus coating thicknesses in the range of 8.0microns to 20.0 microns produced higher tensile strength than averagethicknesses below this range. The higher tensile strength exhibited byExamples 1 and 2 enable use of thinner high-modulus coatings on opticalfibers, such as those used in submarine cables and repeaters.

TABLE 10 Thickness of High-modulus Coating Example No. 1 2 3 4 5 AverageHigh- 10.2 10.7 6.7 6.7 6.0 modulus Coating microns microns micronsmicrons microns Thickness Tensile Strength 89% 93% 4% 26% 24% (100 kpsiscreening rate)

Exemplary Low-Modulus and High-Modulus Coatings

Exemplary low-modulus and high-modulus coatings are discussed below,along with measurements of strength and puncture resistance of thecoatings.

Low Modulus Coating-Composition. The low-modulus coating compositionincludes the formulation given in Table 11 below and is typical ofcommercially available low-modulus coating compositions.

TABLE 11 Reference Low-modulus Coating Composition Component AmountOligomeric Material 50.0 wt % SR504 46.5 wt % NVC 2.0 wt % TPO 1.5 wt %Irganox 1035 1.0 pph 3-Acryloxypropyl trimethoxysilane 0.8 pphPentaerythritol tetrakis(3-mercaptopropionate) 0.032 pphWhere the oligomeric material was prepared as described herein fromH12MDI, HEA, and PPG4000 using a molar ratio n:m:p=3.5:3.0:2.0, SR504 isethoxylated(4)nonylphenol acrylate (available from Sartomer), NVC isN-vinylcaprolactam (available from Aldrich), TPO (a photoinitiator) is(2,4,6-trimethylbenzoyl)-diphenyl phosphine oxide (available from BASF),Irganox 1035 (an antioxidant) is benzenepropanoic acid,3,5-bis(1,1-dimethylethyl)-4-hydroxythiodi -2,1-ethanediyl ester(available from BASF), 3-acryloxypropyl trimethoxysilane is an adhesionpromoter (available from Gelest), and pentaerythritoltetrakis(3-mercaptopropionate) (also known as tetrathiol, available fromAldrich) is a chain transfer agent. The concentration unit “pph” refersto an amount relative to a base composition that includes all monomers,oligomers, and photoinitiators. For example, a concentration of 1.0 pphfor Irganox 1035 corresponds to 1 g Irganox 1035 per 100 g combined ofoligomeric material, SR504, NVC, and TPO.

The oligomeric material was prepared by mixing H12MDI (4,4′-methylenebis(cyclohexyl isocyanate)), dibutyltin dilaurate and2,6-di-tent-butyl-4 methylphenol at room temperature in a 500 mL flask.The 500 mL flask was equipped with a thermometer, a CaCl₂ drying tube,and a stirrer. While continuously stirring the contents of the flask,PPG4000 was added over a time period of 30-40 minutes using an additionfunnel. The internal temperature of the reaction mixture was monitoredas the PPG4000 was added and the introduction of PPG4000 was controlledto prevent excess heating (arising from the exothermic nature of thereaction). After the PPG4000 was added, the reaction mixture was heatedin an oil bath at about 70° C. to 75° C. for about 1 to 1½ hours. Atvarious intervals, samples of the reaction mixture were retrieved foranalysis by infrared spectroscopy (FTIR) to monitor the progress of thereaction by determining the concentration of unreacted isocyanategroups. The concentration of unreacted isocyanate groups was assessedbased on the intensity of a characteristic isocyanate stretching modenear 2265 cm⁻¹. The flask was removed from the oil bath and its contentswere allowed to cool to below 65° C. Addition of supplemental HEA wasconducted to insure complete quenching of isocyanate groups. Thesupplemental HEA was added dropwise over 2-5 minutes using an additionfunnel. After addition of the supplemental HEA, the flask was returnedto the oil bath and its contents were again heated to about 70° C. to75° C. for about 1 to 1½ hours. FTIR analysis was conducted on thereaction mixture to assess the presence of isocyanate groups and theprocess was repeated until enough supplemental HEA was added to fullyreact any unreacted isocyanate groups. The reaction was deemed completewhen no appreciable isocyanate stretching intensity was detected in theFTIR measurement.

High-Modulus Coating-Compositions. Four curable high-modulus coatingcompositions (A, SB, SC, and SD) are listed in Table 12.

TABLE 12 High-modulus Coating Compositions Composition Component A SB SCSD PE210 (wt %) 15.0 15.0 15.0 15.0 M240 (wt %) 72.0 72.0 72.0 62.0M2300 (wt %) 10.0 — — — M3130 (wt %) — 10.0 — — M370 (wt %) — — 10.020.0 TPO (wt %) 1.5 1.5 1.5 1.5 Irgacure 184 (wt %) 1.5 1.5 1.5 1.5Irganox 1035 (pph) 0.5 0.5 0.5 0.5 DC-190 (pph) 1.0 1.0 1.0 1.0PE210 is bisphenol-A epoxy diacrylate (available from Miwon SpecialtyChemical, Korea), M240 is ethoxylated (4) bisphenol-A diacrylate(available from Miwon Specialty Chemical, Korea), M2300 is ethoxylated(30) bisphenol-A diacrylate (available from Miwon Specialty Chemical,Korea), M3130 is ethoxylated (3) trimethylolpropane triacrylate(available from Miwon Specialty Chemical, Korea), TPO (a photoinitiator)is (2,4,6-trimethylbenzoyl)diphenyl phosphine oxide (available fromBASF), Irgacure 184 (a photoinitiator) is 1-hydroxycyclohexyl-phenylketone (available from BASF), Irganox 1035 (an antioxidant) isbenzenepropanoic acid,3,5-bis(1,1-dimethylethyl)-4-hydroxythiodi-2,1-ethanediyl ester(available from BASF). DC190 (a slip agent) is silicone-ethyleneoxide/propylene oxide copolymer (available from Dow Chemical). Theconcentration unit “pph” refers to an amount relative to a basecomposition that includes all monomers and photoinitiators. For example,for high-modulus coating composition A, a concentration of 1.0 pph forDC-190 corresponds to 1 g DC-190 per 100 g combined of PE210, M240,M2300, TPO, and Irgacure 184.

High-Modulus Coatings — Tensile Properties. The Young's modulus, tensilestrength at yield, yield strength, and elongation at yield ofhigh-modulus coatings made from high-modulus compositions A, SB, SC, andSD were measured using the technique described above. The results aresummarized in Table 13.

TABLE 13 Tensile Properties of High-modulus Coatings High-modulusComposition Property A SB SC SD Young's 2049.08 2531.89 2652.51 2775.94Modulus (MPa) Tensile 86.09 75.56 82.02 86.08 Strength (MPa) Yield 48.2161.23 66.37 70.05 Strength (MPa) Elongation 4.60 4.53 4.76 4.87 at Yield(%) Fracture 0.8580 0.8801 0.9471 0.9016 Toughness, K_(c) (MPa*m^(1/2))

The results show that high-modulus coatings prepared from compositionsSB, SC, and SD exhibited higher Young's modulus and higher yieldstrength than the high-modulus coating prepared from comparativecomposition A. Additionally, the high-modulus coatings prepared fromcompositions SB, SC, and SD exhibited higher fracture toughness than thehigh-modulus coating prepared from composition A. The higher valuesexhibited by composition SB, SC, and SD enable use of thinnerhigh-modulus coatings on optical fibers without sacrificing performance.As discussed above, thinner high-modulus coatings reduce the overalldiameter of the optical fiber and provide higher fiber counts in a givencross-sectional area (such as in submarine repeater).

Exemplary Optical Fiber Embodiments

The experimental examples and principles disclosed herein indicate thatsufficiently low attenuation and high puncture resistance properties canbe achieved in a reduced diameter optical fiber by tailoring therefractive index profile and coating properties of the optical fiber.More specifically, the high-modulus coating provides sufficient punctureresistance for the reduced diameter fiber in spite of the smallercross-sectional area.

FIG. 8 is a plot of the dependence of the puncture load in grams versusthe cross-sectional area of the high-modulus coating. The dashed linehas a slope of 0.00263 g/microns² and corresponds to comparative fibershaving a high-modulus coating having an in situ modulus of about 1500GPa. The solid line is a linear fit to measured data for five fibershaving a high-modulus coating with an in situ modulus of about 1850 GPa,The slope is 0.00328 g/microns², which is approximately equal to theslope for the reference fibers multiplied by the ratio of the in situmoduli, 1850/1500. The dotted line represents the modeled dependence ofthe puncture load in grams versus the cross-sectional area of ahigh-modulus coating having an in situ modulus of 2200 GPa. The resultsindicate that an increase in the in situ modulus of the high-moduluscoating enables a reduction in the cross-sectional area and thicknesswithout a significant degradation of the puncture resistance of thesmaller diameter fiber.

Fiber Draw Process

The optical fibers disclosed herein may be formed from a continuousoptical fiber manufacturing process, during which a glass fiber is drawnfrom a heated preform and sized to a target diameter. In fiberscomprising a low-modulus inner coating, the glass fiber is then cooledand directed to a coating system that applies a liquid low-moduluscoating composition to the glass fiber. Two process options are viableafter application of the liquid low-modulus coating composition to theglass fiber. In one process option (wet-on-dry process), the liquidlow-modulus coating composition is cured to form a solidifiedlow-modulus coating, the liquid high-modulus coating composition isapplied to the cured low-modulus coating, and the liquid high-moduluscoating composition is cured to form a solidified high-modulus coating.In a second process option (wet-on-wet process), the liquid high-moduluscoating composition is applied to the liquid low-modulus coatingcomposition, and both liquid coating compositions are curedsimultaneously to provide solidified low-modulus and high-moduluscoatings. After the fiber exits the coating system, the fiber iscollected and stored at room temperature. Collection of the fibertypically entails winding the fiber on a spool and storing the spool.

In some processes, the coating system further applies a pigmented outercoating composition to the high-modulus coating and cures the pigmentedouter coating composition to form a solidified pigmented outer coating.Typically, the pigmented outer coating is an ink layer used to mark thefiber for identification purposes and has a composition that includes apigment and is otherwise similar to the high-modulus coating. Thepigmented outer coating is applied to the high-modulus coating andcured. The high-modulus coating has typically been cured at the time ofapplication of the pigmented outer coating. The low-modulus,high-modulus, and pigmented outer coating compositions can be appliedand cured in a common continuous manufacturing process. Alternatively,the low-modulus and high-modulus coating compositions are applied andcured in a common continuous manufacturing process, the coated fiber iscollected, and the pigmented outer coating composition is applied andcured in a separate offline process to form the pigmented outer coating.

Coating Application, Coating Material Viscosity and Coating Die Size

In some embodiments, optical fiber drawn from a pre-form within a drawfurnace, is passed through a coating system where a polymer coating isapplied to the optical fiber. The coating system may comprise anentrance and a sizing die. Disposed between the entrance and the sizingdie is a coating chamber. The coating chamber is filled with the polymercoating material in liquid form. The optical fiber enters the coatingsystem through the entrance and passes through the coating chamber wherethe polymer coating material is applied to the surface of the opticalfiber. The optical fiber then passes through the sizing die where anyexcess coating material is removed as the optical fiber exits thecoating system to achieve a coated optical fiber of a specified diameterin accordance of some embodiments described herein.

FIG. 12 shows the effects of coating material viscosity and die size onthe coating thickness for a given constant drawing speed (60 m/min inthis case). As shown in FIG. 12 , the coating thickness is mainlyaffected by the diameter of the sizing die, while the coating materialviscosity has only marginal effects. For example, the coated fiberdiameter varies from 127 μm to 169 μm when the sizing die changes from5.1 mil (129.54 μm) to 8.0 mil (203.2 μm), while the coating thicknessonly varies slightly with a wide range of coating material viscositygiven a certain die size. In some embodiments, the viscosity of thecoating material is greater than 20 poise at 50 rpm and 25° C., orgreater than 40 poise at 50 rpm and 25° C.

FIG. 13 depicts an exemplary parameter window for forming a targetedfinal coated diameter of 132±1 μm on a 125 micron glass optical fiber.As shown in FIG. 13 , the sizing die is identified in the range from5.35 mil (135.89 μm) to 5.51 mil (140 μm), while the coating materialviscosity can range widely within the parameter window. Thus, while thecoating material viscosity has only marginal effect on the final coatingthickness, the effective magnitude differs for different die sizesystems. FIG. 14 shows the coating thickness standard deviationresulting from various coating material viscosity for different die sizesystems. FIG. 14 shows that the standard deviation slightly increaseswith increasing die size and rises dramatically when the die size islarger than 7 mil. FIG. 15 depicts the effect of drawing speed oncoating thickness in accordance with some embodiments of the currentdisclosure. As seen in FIG. 15 , the drawing speed of the fiber has onlylimited effects on the coating thickness.

With respect to coating concentricity, lubrication pressure within thecoating die is assumed to act as the centering force to make sure thatthe optical fiber is centered in the coating applicator. A higherlubrication pressure represents a larger centering force, which wouldproduce a better coating concentricity. FIG. 16 depicts a graph plottingthe correlation between lubrication pressure and the die size for aseries of coating material viscosity. FIG. 16 shows that the lubricationpressure decreases with the increasing of die size and increases withthe increasing of the coating material viscosity. In addition, FIG. 17shows the correlation between lubrication pressure and drawing speed. Asshown in FIG. 17 , the lubrication pressure firstly increasingdramatically and then increases at a slow pace with the increasing ofthe drawing speed. Therefore, combined with the viscosity effect on thecoating thickness as discussed above, increasing the drawing speed andusing materials with larger viscosity with a given die size can improvecoating concentricity without degrading the coating thickness quality.

Performance Data for Optical Fibers with Thin Coatings

Key performance metrics for these optical fibers with thin coatingsinclude their total outer diameter, the thickness of the polymericcoating, the number of breaks per unit length in 50 kpsi strengthscreening, and the longest saved lengths after 50 kpsi screening. Ahigh-modulus coating layer was applied onto a 125 μm single mode fiber(SMF) fiber with about 7 μm overall coating thickness (See Table 15 ReelID 121-6599-3 and Reel ID 122-6645-4). The lower the screening force is,the longer the segment of unbroken fiber. The high-modulus coated fiber(Reel ID 121-6599-3) has similar fiber strength to that of the freshhigh-modulus coated fiber (Reel ID 122-6645-4). The inventors have foundthat the thin acrylate hard fiber coating using a fresh high-moduluscoated fiber has concentricity greater than about 70%, and in someembodiments greater than about 80%, or greater than about 85%, orgreater than about 90%, or greater than about 95%.

TABLE 15 Performance Data for Optical Fibers with High-Modulus CoatingReel ID 121-6599-3 121-6599-4 122-6645-3 122-6645-4 Draw Run Data GlassType SMF SMF SMF SMF Glass Diameter (μm) 125 125 125 125 Draw Speed(m/min) 50 50 50 50 Total fiber saved (m) 6000 6000 6000 6160 Totalfiber screened 5000 5000 5000 5000 (m) High-modulus Coating 5.4 6 6 5.4Die Size (mil) High-modulus Coating 132 140 140 132 Diameter (μm) FiberScreening Screen Weight (kpsi) 50 50 50 50 Number of Breaks 22 1 1 21Longest save length 694 4659 4646 396 (m) Number of strip 6 0 0 6sections Meter 217 2500 2500 227 screened/(Number of breaks +1)

Compared to a thin acrylate coating of an aged high-modulus coated fiberapplied onto a 125 μm SMF fiber with about 7 μm overall coatingthickness (See Table 16 Reel ID 121-6602-10 and Reel ID 121-6602-12), afresh high-modulus coated fiber shown in Reel ID 121-6599-3 showed muchhigher number of both the longest save length (m) and the ratio ofmeters of the thin coated fiber screened/(Number of Breaks+1) when thethin coated fibers were screened at 50 kpsi force. The breaks of thesethree fibers are pretty evenly distributed throughout the fiberscreening length. This indicates that the old high-modulus coated fiberis most likely degraded partially during storage. Yet all these threethin acrylate coated fibers have good concentricity (i.e. >70%).

TABLE 16 Performance Data for Optical Fibers with High-Modulus CoatingReel ID 121-6602-10 121-6602-12 Draw Run Data Glass Type SMF SMF GlassDiameter (μm) 125 125 Draw Speed (m/min) 40 35 Total fiber saved (m)1200 1200 Total fiber screened 1200 2950 (m) High-modulus 5.4 5.4Coating Size Die (mil) High-modulus 132 132 Coating Diameter (μm) FiberScreening Screen Weight (kpsi) varied 50 Number of Breaks 27 21 Longestsave length 132 189 (m) Number of strip 4 3 sections Meter 43 134screened/(Number of breaks +1)

A thin acrylate coating of a fresh high-modulus coating layer wasapplied onto a 125 μm SMF fiber with 15 μm overall coating thickness(See Table 15 Reel ID 121-6599-4 and Reel ID 122-6645-3). By increasingthe coating thickness from 7 μm in Reel ID 121-6599-3 to 15 μm in ReelID 121-6599-4 using a fresh high-modulus coating layer, the thin coatedfiber is much stronger as indicated by significant increasing of boththe longest save length (m) and the ratio of meters of the thin coatedfiber screened/(Number of Breaks+1) when the thin coated fibers werescreened at 50 kpsi. By increasing the coating thickness from 7 μm inReel ID 122-6645-4 to 15 μm in Reel ID 122-6645-3 using a freshhigh-modulus coating layer, the thin coated fiber is much stronger asindicated by significant increasing of both the longest save length (m)and the ratio of meters of the thin coated fiber screened/(Number ofBreaks+1) when the thin coated fibers were screened at 50 kpsi force.Furthermore, the thin acrylate hard fiber coating has good concentricity(i.e. >70%). These thin acrylate coated fibers with 15 μm overallcoating thickness (Reel ID 121-6599-4 and Reel ID 122-6645-3 in Table15) are strong enough to survive the ribbon cable process.

A thin two-layer acrylate fiber coating drawing of a fresh low-moduluscoating layer and a fresh high-modulus coating layer was also carriedout (See Table 16 Reel ID 121-6599-5). The thickness of the low-moduluscoating layer is 9 μm and the thickness of the high-modulus coatinglayer is 8 μm. The overall thickness of the low-modulus coating layerplus the high-modulus coating layer thickness is 17 μm. The thinacrylate coating running is smooth and the coating on fiber has nodefects. This thin coated fiber was screened at 50 kpsi and thescreening results are similar to a fresh high-modulus coating layer on125 μm SMF fiber with 15 μm overall coating thickness (See Reel ID121-6599-4 in Table 15). The thin acrylate hard fiber coating has goodconcentricity (i.e. >70%). This thin acrylate coated fiber is alsostrong enough to survive the ribbon cable process. With the presence ofa soft thin low-modulus coating layer, this two-layer thin coated fiberhas improved microbending performance over a one-layer thin hard coatingfiber.

TABLE 17 Performance Data for Optical Fibers with Low-Modulus Coatingand High-Modulus Coating Reel ID 121-6599-5 Draw Run Data Glass Type SMFGlass Diameter (μm) 125 Draw Speed (m/min) 50 Total fiber saved (m) 6300Total fiber screened 5000 (m) Low-modulus 5.4 Coating Die Size (mil)Low-modulus 134 Coating Diameter (μm) High-modulus 6 Coating DieSize(mil) High-modulus 142 Coating Diameter (μm) Fiber Screening ScreenWeight (kpsi) 50 Number of Breaks 3 Longest save length 4652 (m) Numberof strip 0 sections Meter 1250 screened/(Number of breaks +1)

A thin two-layer acrylate fiber coating drawing of a fresh low-moduluscoating layer and a fresh high-modulus coating layer was carried out ona standard single mode fiber on a graded index core with a silica innercladding and an updoped outer cladding with a relative refractive indexprofile as shown in FIG. 18 . The fiber coating parameters and measuredoptical parameters are shown in Table 18 below. The table below showsthree thin coating configurations having low-modulus coatingdiameter/high-modulus coating diameter of 145 μm/175 μm, 140 μm/160 μm,and 0 μm/140 μm. The fiber having a low-modulus coatingdiameter/high-modulus coating diameter of 190 μm/250 μm is the standardcoating used as a control. For the thin coated fibers, the measuredcable cutoff wavelengths, MFDs are similar to the control fibers, whichindicates that the thin coatings did not impact these parameters. Forthe fibers having a low-modulus inner coating diameter/high-moduluscoating diameter of 145 μm/175 μm and 140 μm/160 μm, the attenuation at1310 and 1550 nm is the same as the control fibers, which shows thatthese thin coating configurations did not result in any attenuationpenalty. The attenuation of the fibers having a low-modulus coatingdiameter/high-modulus coating diameter of 0 μm/140 μm is slightly higherthan the other fibers due to the single coating layer but is acceptablefor many applications using short fibers such as data centers.

TABLE 18 Performance Data for Optical Fibers with Low-Modulus Coatingand High-Modulus Coating Diameter of 145 μm/175 μm, 140 μm/160 μm, and 0μm/140 μm Coating diameters 1310 nm 1550 nm Low- 1310 1550 OTDR OTDRmodulus/ Cable nm nm Attenua- Attenua- High- cutoff MFD MFD tion tionFiber ID modulus (nm) (μm) (μm) (dB/km) (dB/km) 142-1918-1001 145 μm/1223.7 9.1 10.3 0.333 0.188 175 μm 142-1918-901 140 μm/ 1190.0 9.0 10.20.332 0.188 160 μm 142-1918-1101  0 μm/ 1218.5 9.0 10.1 0.336 0.195 140μm 142-1918-801 190 μm/ 1208.8 9.1 10.4 0.333 0.188 250 μm 142-1918-1201190 μm/ 1221.0 9.1 10.2 0.333 0.188 250 μm 142-1918-301 145 μm/ 1210.09.0 10.3 0.334 0.188 175 μm 142-1918-201 140 μm/ 1220.0 9.1 10.2 0.3330.188 160 μm 142-1918-401  0 μm/ 1220.0 9.0 10.3 0.337 0.195 140 μm142-1918-101 190 μm/ 1180.0 9.1 10.2 0.333 0.188 250 μm 142-1918-501 140μm/ 1197.0 8.5  9.88 0.333 0.188 160 μm 142-1918-601 145 μm/ 1189.9 9.010.2 0.333 0.188 175 μm 142-1918-701 190 μm/ 1189.1 9.0 10.3 0.333 0.188250 μm

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention. Since modifications combinations,sub-combinations and variations of the disclosed embodimentsincorporating the spirit and substance of the invention may occur topersons skilled in the art, the invention should be construed to includeeverything within the scope of the appended claims and theirequivalents.

1-20. (canceled)
 21. An optical fiber, comprising: a core region; acladding region surrounding the core region, the cladding regioncomprising: an inner cladding directly adjacent to the core region, andan outer cladding surrounding the inner cladding; and a polymer coatingcomprising a high-modulus coating layer surrounding the cladding regionand a low-modulus coating layer disposed between the cladding region andthe high-modulus coating layer, wherein a thickness of the low-modulusinner coating layer is in a range of 4 microns to 20 microns, themodulus of the low-modulus inner coating layer is less than or equal toabout 0.35 MPa, a thickness of the high-modulus coating layer is in arange of 4 microns to 20 microns, the modulus of the high-modulus innercoating layer is greater than or equal to about 1.6 GPa, and wherein apuncture resistance of the optical fiber is greater than 20 g, andwherein a microbend attenuation penalty of the optical fiber is lessthan 0.03 dB/km, and wherein an outer diameter of the coated opticalfiber is less than or equal to 175 microns, wherein the punctureresistance of the optical fiber is calculated by equationP_(R)=P₀+C₁E_(s)A_(s), wherein As is the cross-sectional area of thehigh-modulus coating, wherein E_(S) is the elastic moduli of thehigh-modulus coating, wherein P₀ is a coefficient having a value of 11.3g and C₁ is a coefficient having a value of 2.1 g/MPa/mm², wherein themicrohend attenuation penalty of the optical fiber is calculated byequation:${{MAP} = {C_{0}f_{0}\sigma\frac{f_{RIP}{f_{g}\left( {E_{g},R_{g}} \right)}{f_{p}\left( {E_{p},t_{p}} \right)}}{f_{cs}\left( {\frac{E_{s}}{E_{p}},R_{s},t_{s}} \right)}}},$wherein f₀ is the average lateral pressure of the external surface incontact with the high modulus coating, wherein s is the standarddeviation of the roughness of the external surface in contact with thehigh modulus coating, wherein${C_{0} = {4 \times {10^{25}\left\lbrack \left( \frac{\pi}{4} \right)^{2.625} \right\rbrack}^{- 1}}},{{and}{wherein}}$${f_{g} = \frac{1}{E_{g}^{2}R_{g}^{6}}},{{and}{wherein}}$${f_{p} = \frac{E_{p}}{t_{p}^{2}}},{{and}{wherein}}$${f_{cs} = {\left\lbrack {1 + {\frac{E_{s}}{E_{p}}\left( \frac{t_{s}}{R_{s}} \right)^{3}}} \right\rbrack^{0.375}\left\{ {\frac{E_{s}}{E_{p}}\left\lbrack {R_{s}^{4} - \left( {R_{s} - t_{s}} \right)^{4}} \right\rbrack} \right\}^{0.625}}},$wherein R_(g) is the radius of the glass, R is the outer radius of thehigh-modulus outer coating, t_(p) is the thickness of the innerlow-modulus coating, t_(s) is the thickness of the high-modulus outercoating, E_(g) is the elastic moduli of the glass, E_(p) is the elasticmoduli of the low-modulus inner coating, and E_(S) is the elastic moduliof the high-modulus coating.
 22. The optical fiber of claim 21, whereinthe core region comprises silica glass doped with GeO₂.
 23. The opticalfiber of claim 22, wherein the core region has a relative refractiveindex Δ_(1max) in the range from 0.25% to 0.40%.
 24. The optical fiberof claim 22, wherein the core region has a radius ri in the range from4.0 microns to 6.0 microns.
 25. The optical fiber of claim 21, whereinthe inner cladding region has a relative refractive index 42 in therange from −0.05% to 0.05%.
 26. The optical fiber of claim 21, whereinthe inner cladding region has a radius r₂ in the range from 9.0 micronsto 15.0 microns.
 27. The optical fiber of claim 21, wherein the claddingregion further comprises a depressed-index cladding region between theinner cladding region and the outer cladding region, the depressed-indexcladding region having a relative refractive index Δ₃ less than therelative refractive index Δ₂ of the inner cladding region and therelative refractive index Δ₄ of the outer cladding region.
 28. Theoptical fiber of claim 27, wherein the depressed-index cladding regionhas a relative refractive index Δ₃ in the range from −0.30% to -0.80%.29. The optical fiber of claim 27, wherein the depressed-index claddingregion has a radius r₃ in the range from 14.0 microns to 18.0 microns.30. The optical fiber of claim 21, wherein the outer cladding region hasa radius r₄ in the range from 60.0 microns to 65.0 microns.
 31. Theoptical fiber of claim 21, wherein the outer cladding region has aradius r₄ in the range from 61.0 microns to 64.0 microns.
 32. Theoptical fiber of claim 21, wherein the outer cladding region has aradius r₄ in the range from 62.0 microns to 63.0 microns.
 33. Theoptical fiber of claim 21, wherein the thickness of the high-moduluscoating is in the range from 9 microns to 18 microns.
 34. The opticalfiber of claim 21, wherein the total thickness of the low-moduluscoating and the high-modulus coating is 25 microns or less.
 35. Theoptical fiber of claim 21, wherein the outer diameter of the coatedoptical fiber is between 155 microns and 175 microns.
 36. The opticalfiber of claim 21, wherein the outer diameter of the coated opticalfiber is between 160 microns and 170 microns.
 37. The optical fiber ofclaim 21, wherein the microbend attenuation penalty of the optical fiberis ≤0.01 dB/km.
 38. The optical fiber of claim 21, wherein the microbendattenuation penalty of the optical fiber is ≤0.007 dB/km.
 39. Theoptical fiber of claim 21, wherein the microbend attenuation penalty ofthe optical fiber is ≤0.003 dB/km.
 40. The optical fiber of claim 21,wherein the puncture resistance of the optical fiber is ≥26 g.
 41. Theoptical fiber of claim 21, wherein the puncture resistance of theoptical fiber is ≥34 g.
 42. The optical fiber of claim 21, wherein anattenuation of the optical fiber at 1550 nm is less than 0.20 dB/km. 43.The optical fiber of claim 21, wherein a mode field diameter of theoptical fiber at 1310 nm is ≥8.6 microns.